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Python Program to Find the Sum of the Series 1 + 2 + 3 + ... + N / Sum of the First N Natural Numbers

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Sum of series

Python programs to find the sum of the series $1 + 2 + 3 + ... + n$ i.e. the sum of the first $n$ natural numbers have been shown here. Both the iterative and recursive approaches have been shown below. The sum can also be computed using the mathematical formula $\frac{n(n+1)}{2}$.


Example:

Suppose $n = 7$

So the sum of first $7$ natural numbers = $1 + 2 + 3 + 4 + 5 + 6 + 7 = 28$

By using the mathematical formula, we obtain the sum of first $7$ natural numbers = $\frac{7 \cdot (7+1)}{2} = 28 $


The algorithm, pseudocode and time-complexity of the program have also been covered in the following sections.






1. Algorithm to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers


1. Take number of terms $n$ as input.

2. Set $sum = 0$.

3. Add each $i \in [1, n]$, to $sum$.

4. Display $sum$ as output.




2. Pseudocode to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers


Input: Number of terms $n$

Output: Sum of $1+2+3+...+n$

1. Procedure sumSeries($n$):

2. $sum \leftarrow 0$:

3. Repeat for each $i \in [1, n]$:

4. $sum \leftarrow sum + i$

5. Return $sum$

6. End Procedure





3. Time complexity to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers


Time Complexity: O(n)

Here $n$ is the number of terms.


Time Complexity (Using formula): O(1)




4. Program & output to find the sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers




4.1. Python Program & output to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using formula

Code has been copied
# ***********************************************
#               alphabetacoder.com
# Python program to find sum of series 1 + 2 + 3
# +...+n using the formula n(n + 1) / 2
# ***********************************************

# initialize
s = 0

# take no of terms as input
n = int(input("Enter no of terms: "))

# calculate the sum using formula
s = (n * (n + 1)) // 2

# display result
print("Sum =", s)

Output

Enter no of terms: 75

Sum = 2850





4.2. Python Program to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using iteration

Code has been copied
# ***********************************************
#               alphabetacoder.com
# Python program to find sum of series 1 + 2 + 3
# +...+n using iterative approach
# ***********************************************

# initialize
s = 0

# take no of terms as input
n = int(input("Enter no of terms: "))

# calculate the sum using loop
for i in range(1, n + 1):
    s = s + i

# display result
print("Sum =", s)

Output

Enter no of terms: 30

Sum = 465





4.3. Python Program to find sum of the series 1 + 2 + 3 + ... + n / Sum of the First N Natural Numbers using recursion

Code has been copied
# ***********************************************
#               alphabetacoder.com
# Python program to find sum of series 1 + 2 + 3
# +...+n using iterative approach
# ***********************************************

# recursive function to calculate sum
# of series 1 + 2 + 3 ... + n
def calculate_sum(n):
    # exit condition of recursive call
    if n == 0:
        return 0

    # call function
    return n + calculate_sum(n - 1)


# declare a main function
def main():
    # take no of terms as input
    n = int(input("Enter no of terms: "))

    # call recursive function
    # to calculate sum
    # display the result
    print("Sum =", calculate_sum(n))


# driver code
main()

Output

Enter no of terms: 100

Sum = 5050





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