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Onyejiaku Theophilus Chidalu

The **sum of the squares** of the first n natural numbers involves calculating the sum of squares from 1 to n.

Mathematically, the formula for the sum of squares of the first n natural numbers is given as follows:

$\sum_{i=1}^n$ $i^{2}$ = $1^{2}$ + $2^{2}$ + $3^{2}$ + $4^{2}$ + … + $n^{2}$

In this shot, we will write a simple program that calculates the sum of the squares of the first n natural numbers.

We will solve this problem using the `while`

and `for`

loops.

`while`

loopThe following code calculates the sum of the first n natural numbers using the `while`

loop:

#include<iostream> using namespace std; int main() { int sum = 0, i = 1, n = 5; // iterating i from 1 to n while (i <= n) { // finding square of i and adding to sum sum += i * i; i++; } // displaying the final result cout << "The sum of squares of first " << n << " numbers is: " << sum << endl; return 0; }

The `while`

loop provides a condition that while `i`

is less than `n`

, the program will calculate the sum of squares using an increment for the squares sequentially. So it provides an increment in *line 10* and also an increment of the numbers (preceding the value of n) by one in *line 11*.

`for`

loopThe following code calculates the sum of the first n natural numbers using a `for`

loop:

#include<iostream> using namespace std; int main() { int sum = 0, n = 5; // iterating i from 1 to n for (int i = 1; i <= n; i++) { // finding square of i and adding to sum sum += i * i; } // displaying the final result cout << "The sum of squares of first " << n << " numbers is: " << sum << endl; return 0; }

This is how we can successfully create a program to compute the sum of squares of the first n natural numbers with a `for`

loop.

RELATED TAGS

c++

sum

squares

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Onyejiaku Theophilus Chidalu

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