In this article we will show you, How to write a C Program to Find Sum of series 1²+2²+3²+….+n² using For Loop, and Functions with example. Before we get into the example, The Mathematical formula for Sum of series 1²+2²+3²+….+n² = ( n (n+1) (2n+1)) / 6

## C Program to Find Sum of series 1²+2²+3²+….+n²

In this C program user is asked to enter any positive integer and then using that value, compiler will find the sum of series 1^{2} + 2^{2} + 3^{2} + … + n^{2} using the above formula.

/* C Program to Calculate Sum of series 1²+2²+3²+....+n² */ #include <stdio.h> int main() { int Number, Sum = 0; printf("\n Please Enter any positive integer \n"); scanf(" %d",&Number); Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6; printf("\n The Sum of Series for %d = %d ",Number, Sum); }

**OUTPUT**

**ANALYSIS**

Within the main() function,

We declared 2 integer variables Number and Sum. Below printf statement will ask the user to enter any integer value.

printf("\n Please Enter any positive integer \n");

scanf(" %d",&Number);

In the next line, We are calculating the Sum of the series 1²+2²+3²+4²+5² using above formula

Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6;

Sum = (5 * (5 + 1) * (2 * 5 +1)) / 6

Sum = (5 * 6 * 11) / 6

Sum = 330 /6

Sum = 55

Final printf statement will print the Sum as output

printf("\n The Sum of Series for %d = %d ", Number, Sum);

The Sum of Series for 5 = 55

## C Program to calculate Sum of series 1²+2²+3²+….+n²

If you want to display the series order 1^{2} + 2^{2} + 3^{2} +4^{2} + 5^{2 }in the output then we have to add extra For loop to display as below

/* C Program to Calculate Sum of series 1²+2²+3²+....+n² */ #include <stdio.h> int main() { int Number, i, Sum = 0; printf("\nPlease Enter any positive integer \n"); scanf("%d",&Number); Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6; for(i =1; i<=Number;i++) { if (i != Number) printf("%d^2 + ",i); else printf("%d^2 = %d ",i, Sum); } }

**OUTPUT**

**ANALYSIS**

We declared 3 integer variables Number, i and Sum. For loop inside the main function will traverse each and every member and displays the output

for(i =1; i<=Number; i++) { if (i != Number) printf("%d^2 + ",i); else printf("%d^2 = %d ",i, Sum); }

Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6;

Sum = (4 * (4 + 1) * (2 * 4 +1))/6

Sum = (4 * 5 * 9) / 6

= 180 /6

Sum = 30

Now the compiler will enter into for loop

**First Iteration**

i = 1 so the condition inside the for loop (i <= Number) is TRUE (1 <=4).

Next, It will go to if condition (i != Number). It means

(1 != 4) – Which is TRUE So, it will print the output as 1²+

i is incremented to 2.

It will do the same until i reaches 4. When it reached 4 then if condition will fails so, Else statement is printed.

The final Output will be 1²+2²+3²+4² = 30

## C Program to Find Sum of series 1²+2²+3²+….+n² using Functions

In this C program user is asked to enter any positive integer and then using that value, compiler will find the sum of series 1^{2} + 2^{2} + 3^{2} + … + n^{2} using functions.

/* C Program to Calculate Sum of series 1²+2²+3²+....+n² */ #include <stdio.h> void Sum_Of_Series(int); int main() { int Number; printf("\n Please Enter any positive integer \n"); scanf("%d",&Number); Sum_Of_Series(Number); } void Sum_Of_Series(int Number) { int i, Sum; Sum = (Number * (Number + 1) * (2 * Number + 1 )) / 6; for(i =1;i<=Number;i++) { if (i != Number) printf("%d^2 + ",i); else printf(" %d^2 = %d ", i, Sum); } }

**OUTPUT**

**ANALYSIS**

void Sum_Of_Series(int);

First line of the program is the declaration of User Defined Function

Within the main() function,

We declared 1 integer variable Number. Below printf statement will ask the user to enter any integer value.

printf(" \n Please Enter any positive integer \n");

Below scanf statement will assign the user integer value to the variable name Number

scanf("%d",&Number);

In the next line, we called the user defined function Sum_Of_Series().

Sum_Of_Series(Number);

When the compiler reaches the function calling then it will jump to the function definition for the calculations. We already explained the logic in the above example.

## C Program to Find Sum of series 1²+2²+3²+….+n² using Recursion

Please refer Find Sum of series 1²+2²+3²+….+n² using Recursion in Recursion Article to see the code and working principle.

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