Как найти сумму чисел фибоначчи python

What is the Fibonacci Series?

According to Google Fibonacci Series is a series of numbers

in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The next number is found by adding up the two numbers before it.

• The 2 is found by adding the two numbers before it (1+1)
• The 3 is found by adding the two numbers before it (1+2),
• And the 5 is (2+3),
• and so on!

It is that simple!

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, …

Can you figure out the next few numbers?

History

The Fibonacci sequence appears in Indian mathematics in connection with Sanskrit prosody, as pointed out by Parmanand Singh in 1985.^[8][10][11] In the Sanskrit poetic tradition, there was interest in enumerating all patterns of long (L) syllables of 2 units duration, juxtaposed with short (S) syllables of 1 unit duration. Counting the different patterns of successive L and S with a given total duration results in the Fibonacci numbers: the number of patterns of duration m units is F_m + 1.^[9]

Knowledge of the Fibonacci sequence was expressed as early as Pingala (c. 450 BC–200 BC). Singh cites Pingala’s cryptic formula misrau cha (“the two are mixed”) and scholars who interpret it in context as saying that the number of patterns for m beats (F_m+1) is obtained by adding one [S] to the F_m cases and one [L] to the F_m−1 cases. Bharata Muni also expresses knowledge of the sequence in the Natya Shastra (c. 100 BC–c. 350 AD). However, the clearest exposition of the sequence arises in the work of Virahanka (c. 700 AD), whose own work is lost, but is available in a quotation by Gopala (c. 1135)

About Fibonacci The Man

His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.

“Fibonacci” was his nickname, which roughly means “Son of Bonacci”.

As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0,1,2,3,4,5,6,7,8,9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble! Thank you, Leonardo.

Also Read: How Instagram Is Using Django And Python

Fibonacci Day is November 23rd, as it has the digits “1, 1, 2, 3” which is part of the sequence. So next Nov 23 let everyone know!

The Rule for Fibonacci Series

The Fibonacci Sequence can be written as a “Rule”

First, the terms are numbered from 0 onwards like this:

So term number 6 is called x₆ (which equals 8).

So we can write the rule:

The Rule is x_n = x_n-1 + x_n-2

where:

• Here x_n is term number “n”
• x_n-1 is the previous term (n-1)
• And x_n-2 is the term before that (n-2)

Python Program for Fibonacci Series/ Sequence

Python Program for Fibonacci Series using Iterative Approach

This approach is based on the following algorithm
1. Declare two variables representing two terms of the series. Initialize them to 0 and 1 as the first and second terms of the series respectively.
2. Initialize a variable representing loop counter to 0.
3. Loop from 0 to the total number of terms in the series.
4. In every iteration,
A. add the variables defined in step 1. This represents a term(or item) of the Fibonacci series.
B. assign the value of the second variable to first and the sum in above step A to the second variable.
So Python program to generate Fibonacci series written as per the above algorithm follows.

def fibonacci(num):
    num1 = 0
    num2 = 1
    series = 0
    for i in range(num):
        print(series, end=' ');
        num1 = num2;
        num2 = series;
        series = num1 + num2;


# running function after takking user input
num = int(input('Enter how many numbers needed in Fibonacci series- '))
fibonacci(num)

Thus the Output of the Execution is:

Enter how many numbers needed in Fibonacci series –
6
0,1,1,2,3,5,

Python Program for Fibonacci Series using recursion

Create a recursive function which receives an integer as an argument. This integer argument represents the position in Fibonacci series and returns the value at that position. Thus, if it receives 5, it returns the value at 5th position in Fibonacci series.
This recursive function returns 0 and 1 if the argument value is 0 or 1. For all other values, it calls itself with the sum of nth and (n-1)th positions.
The program reads the total number of elements in Fibonacci series from the keyboard. It then initiates a loop starting from 0 till this input value. In every iteration, the recursive function is called and the resultant Fibonacci item for that position is printed.

def fibonacci(number):
    # return 0 and 1 for first and second terms
    if number == 0:
        return 0
    elif number == 1:
        return 1
    else:
        # return the sum of two numbers
        return fibonacci(number - 1) + fibonacci(number - 2)
 
# read the total number of items in Fibonacci series
max_item_input = input("Enter the number of items in Fibonacci seriesn")
max_item = int(max_item_input)
 
# iterate from 0 till number of terms
for count in range(max_item):
    print(fibonacci(count), end=",")

Thus the output of the above execution is

Enter the number of items in Fibonacci series
8
0,1,1,2,3,5,8,13,

Applications of Fibonacci Series / Sequence / Number

• First of all the Fibonacci numbers are important in the computational run-time analysis of Euclid’s algorithm to determine the greatest common divisor of two integers: the worst case input for this algorithm is a pair of consecutive Fibonacci numbers.
• The Fibonacci numbers are also an example of a complete sequence. So, this means that every positive integer can be written as a sum of Fibonacci numbers, where anyone number is used once at most.
• Fibonacci numbers are used by some pseudorandom number generators.
• They are also used in planning poker, which is a step in estimating software development projects that use the Scrum methodology.
• Also, Fibonacci numbers arise in the analysis of the Fibonacci heap data structure.
• Retracement of Fibonacci levels is widely used in technical analysis for financial market trading.

So, I hope you liked this article and if you have any questions/recommendations or just want to say hi, comment below!

Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: Exploring the Fibonacci Sequence With Python

The Fibonacci sequence is a pretty famous sequence of integer numbers. The sequence comes up naturally in many problems and has a nice recursive definition. Learning how to generate it is an essential step in the pragmatic programmer’s journey toward mastering recursion. In this tutorial, you’ll focus on learning what the Fibonacci sequence is and how to generate it using Python.

In this tutorial, you’ll learn how to:

• Generate the Fibonacci sequence using a recursive algorithm
• Optimize the recursive Fibonacci algorithm using memoization
• Generate the Fibonacci sequence using an iterative algorithm

To get the most out of this tutorial, you should know the basics of Big O notation, object-oriented programming, Python’s special methods, conditional statements, functions, and basic data structures like lists, queues, and stacks. Having some familiarity with these concepts will greatly help you understand the new ones you’ll be exploring in this tutorial.

Let’s dive right in!

>>> def fibonacci_of(n):
...     if n in {0, 1}:  # Base case
...         return n
...     return fibonacci_of(n - 1) + fibonacci_of(n - 2)  # Recursive case
...

>>> [fibonacci_of(n) for n in range(15)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

>>> cache = {0: 0, 1: 1}

>>> def fibonacci_of(n):
...     if n in cache:  # Base case
...         return cache[n]
...     # Compute and cache the Fibonacci number
...     cache[n] = fibonacci_of(n - 1) + fibonacci_of(n - 2)  # Recursive case
...     return cache[n]

>>> [fibonacci_of(n) for n in range(15)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

 1# fibonacci_class.py
 2
 3class Fibonacci:
 4    def __init__(self):
 5        self.cache = [0, 1]
 6
 7    def __call__(self, n):
 8        # Validate the value of n
 9        if not (isinstance(n, int) and n >= 0):
10            raise ValueError(f'Positive integer number expected, got "{n}"')
11
12        # Check for computed Fibonacci numbers
13        if n < len(self.cache):
14            return self.cache[n]
15        else:
16            # Compute and cache the requested Fibonacci number
17            fib_number = self(n - 1) + self(n - 2)
18            self.cache.append(fib_number)
19
20        return self.cache[n]

>>> from fibonacci_class import Fibonacci

>>> fibonacci_of = Fibonacci()

>>> fibonacci_of(5)
5
>>> fibonacci_of(6)
8
>>> fibonacci_of(7)
13

>>> [fibonacci_of(n) for n in range(15)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

 1# fibonacci_func.py
 2
 3def fibonacci_of(n):
 4    # Validate the value of n
 5    if not (isinstance(n, int) and n >= 0):
 6        raise ValueError(f'Positive integer number expected, got "{n}"')
 7
 8    # Handle the base cases
 9    if n in {0, 1}:
10        return n
11
12    previous, fib_number = 0, 1
13    for _ in range(2, n + 1):
14        # Compute the next Fibonacci number, remember the previous one
15        previous, fib_number = fib_number, previous + fib_number
16
17    return fib_number

>>> from fibonacci_func import fibonacci_of

>>> fibonacci_of(5)
5
>>> fibonacci_of(6)
8
>>> fibonacci_of(7)
13

>>> [fibonacci_of(n) for n in range(15)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: Exploring the Fibonacci Sequence With Python

In this python tutorial, you will learn about the Python Fibonacci series, we will see the Python program to print Fibonacci series and also we will check:

• fibonacci series in python
• Python program to print fibonacci series using recursion
• fibonacci series in python using for loop
• Python program to print fibonacci series up to n terms
• Python program to print fibonacci series between 0 to 50
• Python program to print fibonacci series using iteration
• Python program to print fibonacci series without using recursion
• Python program to print fibonacci series until ‘n’ value using recursion
• print fibonacci series in python using while loop
• Python program to print fibonacci series using function
• Program to print first 50 fibonacci numbers in python
• Python program to print fibonacci series in python using a list
• fibonacci series in python using function

Now, we will see python program to print fibonacci series.

• In this example, I have used the function def fib(n)
• We have initialized the first term to 0 and the second term to 1.
• The for loop is used to iterate the values till the given number
• At last, it will print fibonacci series

Example:

def fib(n):
    a = 0
    b = 1
    if n == 1:
        print(a)
    else:
        print(a)
        print(b)
        for i in range(2,n):
            c = a + b
            a = b
            b = c
            print(c)
fib(10)

To get the output, I have used print(c) to get the Fibonacci series. You can refer to the below screenshot for the output.

The above code, we can use to print fibonacci series in Python.

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Python program to print fibonacci series using recursion

Here, we will see python program to print fibonacci series using recursion.

• In this example, I have used the function def Fibonacci(number)
• Here, if (number == 0) check whether the given number is 0 or not. If it is true, the function returns the value zero.
• elif (number == 1) check whether the given number is 1 or not. If it is true, the function returns the value one.
• A recursive function Fibonacci() is used to calculate the n term sequence.
• A for loop is used to iterate and calculate each term recursively.
• We will take the input from the user

Example:

def Fibonacci(number):
           if(number == 0):
                      return 0
           elif(number == 1):
                      return 1
           else:
                      return (Fibonacci(number - 2)+ Fibonacci(number - 1))
number = int(input("Enter the Range Number: "))
for n in range(0, number):
           print(Fibonacci(n))

To get the output, I have used print(Fibonacci(n)) to get the fibonacci series using recursion. You can refer to the below screenshot for the output.

The above code we can use to print fibonacci series using recursion in Python.

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Fibonacci series in python using for loop

Let’s see python program to print fibonacci series using for loop

• Firstly, we will allow the user to enter any positive integer.
• We have initialized the First_val to 0 and the second_val to 1.
• Here, for loop is used to iterate the number from 0 to user-specified number.
• At last, print(next) is used to get the fibonacci series in Python

Example:

Below is an example of fibonacci series in python using for loop.

num = int(input("Enter the Range Number: "))
First_val = 0
Second_val = 1
for n in range(0, num):
           if(n <= 1):
                      next = n
           else:
                      next = First_val + Second_val
                      First_val = Second_val
                      Second_val = next
           print(next)

To get the output, I have used print(next) to get the fibonacci series using for loop. You can refer to the below screenshot for the output.

The above code, we can use to print fibonacci series using for loop in Python.

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Python program to print fibonacci series up to n terms

Here, we will see python program to print fibonacci series up to n terms

• Firstly, we will allow the user to enter n terms
• We have initialized n1 to 0 and n2 to 1.
• If the number of terms is more than 2, we will use a while loop to find the next term in the sequence by adding the preceding two terms.
• After that, we interchange the variable and continue with the process.

Example:

n = int(input("Enter the n terms: "))
n1, n2 = 0, 1
count = 0
if n <= 0:
   print("Please enter a positive integer")
elif n == 1:
   print("Fibonacci sequence upto",n,":")
   print(n1)
else:
   print("Fibonacci sequence:")
   while count < n:
       print(n1)
       r = n1 + n2
       n1 = n2
       n2 = r
       count += 1

To get the output, I have used print(Fibonacci sequence) to get the fibonacci series up to n terms. You can refer to the below screenshot for the output

This is the Python program to print fibonacci series up to n terms.

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Python program to print fibonacci series between 0 to 50

Now, we will see python program to print fibonacci series between 0 to 50

• We have initialized n1 to 0 and n2 to 1.
• Every next number is found by adding up the two numbers before it.

Example:

n1,n2 = 0,1
print(n1)
while n2<50:
    print(n2)
    n1,n2 = n2, n1+n2

To get the output, I have used print to get the fibonacci series between 0 to 50. You can refer to the below screenshot for the output.

The above Python code, we can use to print fibonacci series between 0 to 50 in Python.

Python program to print fibonacci series using iteration

Now, we will see python program to print fibonacci series using iteration.

• In this example, I have used the function def fib(number).
• We have initialized first as 0 and second as 1.
• The while loop is used to find the next term in the sequence by adding the preceding two terms.
• And then update the value of the first and second.

Example:

def fib(number):
   count = 0
   first = 0
   second = 1
   temp = 0
   while count <= number:
      print(first)
      temp = first + second
      first = second
      second = temp
      count = count + 1
fib(6)

To get the output, I have used print to get the fibonacci series using iteration. You can refer to the below screenshot for the output.

The above Python code, we can use to print fibonacci series using iteration in Python.

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Python program to print Fibonacci series without using recursion

Let’s see python program to print fibonacci series without using recursion.

• Firstly, the user will enter the first two numbers of the series and the number of terms to be printed from the user.
• Then print the first two numbers
• The while loop is used to find the sum of the first two numbers and then the fibonacci series
• Now, print the fibonacci series till n-2 is greater than 0.

Example:

n1=int(input("Enter the first number of the series: "))
n2=int(input("Enter the second number of the series: "))
n=int(input("Enter the number of terms needed: "))
print(n1,n2,end=" ")
while(n-2):
    t=n1+n2
    n1=n2
    n2=t
    print(n2,end=" ")
    n=n-1

To get the output, I have used print to get the fibonacci series without using recursion. You can refer to the below screenshot for the output.

The above Python code we can use to print fibonacci series without using recursion in Python.

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Python program to print fibonacci series until ‘n’ value using recursion

Let see python program to print fibonacci series until ‘n’ value using recursion.

• In this example, I have used the function def recursion_fib(num)
• Here, if num <= 1 then return num
• The other terms are obtained by adding the preceding two terms. The n term is the sum of (num-1) and (num-2) terms.
• A recursive function recursion_fib is used to calculate the n term sequence.
• A for loop is used to iterate and calculate each term recursively.

Example:

def recursion_fib(num):
   if num <= 1:
       return num
   else:
       return(recursion_fib(num-1) + recursion_fib(num-2))
n = 9
if n <= 0:
   print("Plese enter a positive integer")
else:
   print("Fibonacci sequence:")
   for i in range(n):
       print(recursion_fib(i))

To get the output, I have used print(recursion_fib(i)) to get the fibonacci series until ‘n’ value using recursion. You can refer to the below screenshot for the output.

The above code we can use to print fibonacci series until ‘n’ value using recursion in Python.

print fibonacci series in python using while loop

Now, we will see python program to print fibonacci series using while loop.

• Firstly, the user will enter any positive integer.
• We have initialized F_val as 0 and S_val as 1.
• We have declared three integer variables like i, F_val, and S_val.
• The while loop makes sure that the loop starts from 0 and is less than the user given number.
• Within the while loop, we have used if and else.
• And at last fibonacci series will get printed in the output.

Example:

Num = int(input("Enter the Range Number: "))
i = 0
F_val = 0
S_val = 1
while(i < Num):
           if(i <= 1):
                      Next = i
           else:
                      Next = F_val + S_val
                      F_val = S_val
                      S_val = Next
           print(Next)
           i = i + 1

To get the output, I have used print(Next) to get the fibonacci series using a while loop. You can refer to the below screenshot for the output.

The above code, we can use to print fibonacci series using while loop in Python.

Also read, Python For Loop with Examples and Python While Loop Example.

fibonacci series in python using function

Here, we will see python program to print fibonacci series using function

• In this example, we have used the function as def fib(n)
• We have initialized the n1 to 0 and n2 to 1.
• if n == 1 then print(n1)
• The for loop is used to iterate the values till the given number
• At last, it will print fibonacci series

Example:

def fib_series(n):
    n1 = 0
    n2 = 1
    if n == 1:
        print(n1)
    else:
        print(n1)
        print(n2)
        for i in range(2,n):
            t = n1 + n2
            n1 = n2
            n2 = t
            print(t)
fib_series(5)

To get the output, I have used print(t) to get the fibonacci series using function. You can refer to the below screenshot for the output.

Program to print first 50 fibonacci numbers in python

Is anyone asking you to write a python program to get the fibonacci series between 0 to 50? Let’s see the program to print the first 50 fibonacci numbers in python.

• In this example, I have used the function def FibonacciNum(n)
• We have initialized the n1 to 0 and n2 to 1.
• Here, if n < 1 then return
• The for loop is used to iterate the values till the given number.
• At last, call the function FibonacciNum(50) to get the first 50 fibonacci numbers in the output.

Example:

def FibonacciNum(n):
    n1 = 0
    n2 = 1
    if (n < 1):
        return
    print(n1, end=" ")
    for i in range(1, n):
        print(n2, end=" ")
        next = n1 + n2
        n1 = n2
        n2 = next
FibonacciNum(50)

You can refer to the below screenshot for the output of first 50 fibonacci numbers in python.

Python program to print fibonacci series in python using a list

Now, we will see python program to print fibonacci series in python using a list

• Firstly, the user will enter any positive integer.
• The for loop is used to iterate the values till the given number
• At last, print(fib) to get the fibonacci series in the list.

Example:

n = int(input("Enter the number:"))
if n==0:
    fib=[0]
elif n==1:
    fib=[0,1]
else:
    fib=[0,1]
    for i in range(2,n):
        fib.append(fib[i-1]+fib[i-2])
print(fib)

To get the output, I have used print(fib) to get the fibonacci series using function. You can refer to the below screenshot for the output.

The above code we can use to to print fibonacci series using function in Python.

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In this Python tutorial, we have learned about the Python program to print Fibonacci series or Fibonacci Series in Python. Also, we covered these below topics:

• Python program to print fibonacci series
• Fibonacci series in python using recursion
• Python program to print fibonacci series using for loop
• Python program to print fibonacci series up to n terms
• Python program to print fibonacci series between 0 to 50
• Python program to print fibonacci series using iteration
• Fibonacci series in python without recursion
• Python program to print fibonacci series until ‘n’ value using recursion
• Python program to print fibonacci series using while loop
• Python program to print fibonacci series using function
• Program to print first 50 fibonacci numbers in python
• Python program to print fibonacci series in python using a list