Python Program to Print the Natural Numbers Summation Pattern

Last Updated : 13 Dec, 2025

Given a natural number n, the task is to print a pattern where each line shows the summation of the first k natural numbers (for all k from 1 to n) along with the total of those values. For Example:

Input: n = 5
Output:
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

Let’s explore different methods to generate this summation pattern.

Using Mathematical Formula

The sum of first j natural numbers is computed using the direct formula j * (j + 1) // 2, and the expression string is built using join().

Python 
n = 5

for j in range(1, n + 1):
    expr = " + ".join(str(i) for i in range(1, j + 1))
    total = j * (j + 1) // 2
    print(expr, "=", total)

Output
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

Explanation:

  • " + ".join(str(i) for i in range(1, j + 1)) builds the expression from 1 to j.
  • j * (j + 1) // 2 uses the mathematical formula to compute the total.

Using Running Sum

A cumulative variable is updated by adding the current number j on each iteration, and the summation expression is formed using join().

Python 
n = 5
s = 0

for j in range(1, n + 1):
    s += j
    expr = " + ".join(str(i) for i in range(1, j + 1))
    print(expr, "=", s)

Output
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

Explanation:

  • s += j updates the cumulative total for each line.
  • join() creates the summation pattern string.

Using sum()

The numbers up to j are generated using range(), converted into a list, and summed using sum() while the expression is built using join().

Python 
n = 5

for j in range(1, n + 1):
    nums = list(range(1, j + 1))
    expr = " + ".join(str(i) for i in nums)
    print(expr, "=", sum(nums))

Output
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

Explanation:

  • list(range(1, j + 1)) creates numbers needed for each line.
  • sum(nums) computes the total.
  • join() builds the final printed expression.

Using Iterative Printing

Numbers are printed one by one along with "+" when needed, while each value is stored inside a list and later summed.

Python 
n = 5

for j in range(1, n + 1):
    a = []
    for i in range(1, j + 1):
        print(i, end=" ")
        if i < j:
            print("+", end=" ")
        a.append(i)
    print("=", sum(a))

Output
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

Explanation:

  • print(i, end=" ") prints each number.
  • The condition if i < j: prints "+" between terms.
  • sum(a) calculates the total of the collected numbers.
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