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 12 + 22 + 32 + … + n2 using the above formula.
CODE
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#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.
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printf("\n Please Enter any positive integer \n"); |
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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
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printf("\n The Sum of Series for %d = %d ", Number, Sum); |
The Sum of Series for 5 = 55
Method 2 to Find Sum of series 1²+2²+3²+….+n²
If you want to display the series order 12 + 22 + 32 +42 + 52 in the output then we have to add extra For loop in C Programming to display as below
CODE
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#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
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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
Sum = 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 12 + 22 + 32 + … + n2 using functions.
CODE
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#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
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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.
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printf(" \n Please Enter any positive integer \n"); |
Below scanf statement will assign the user integer value to the variable name Number
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scanf("%d",&Number); |
In the next line, we called the user defined function Sum_Of_Series().
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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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#include<stdio.h>
int main(){
int i,n,sum=0;
printf("take the input upto which we have to find the sum of series\n");
scanf("%d",&n);
i=1;
while(i<=n){
sum=sum+i*i;
++i;
}
printf("%d\n",sum);
}