Tutorial Gateway

C Program to Find Sum of series 1³+2³+3³+….+n³

by

In this article we will show you, How to write a C Program to Find Sum of series 1³+2³+3³+….+n³ using For Loop, Recursion, and Functions with example. This series is also called as Sum of cubes of n natural numbers. The Mathematical formula for Sum of series 1³+2³+3³+….+n³ = ( n (n+1) / 6)²

C Program to Find Sum of series 1³+2³+3³+….+n³

In this C program user is asked to enter any positive integer and then using that value, compiler will find the sum of series 1³+2³+3³+….+n³ using the above formula.

/* Sum of Cubes of n Natural Numbers */

#include <stdio.h>
#include <math.h>

int main()
{
  int Number, Sum = 0;

  printf("\n Please Enter any positive integer \n");
  scanf(" %d",&Number);

  Sum = pow(((Number * (Number + 1))/ 2), 2);
 
  printf("\n The Sum of Series for %d = %d ",Number, Sum);

}

OUTPUT

C Program to Find Sum of series 1³+2³+3³+....+n³

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");

Below scaf statement wil assign the user integer value to the variable name Number

scanf(" %d",&Number);
In the next line, We are calculating the Sum of the series 1³+2³+3³+4³+5³ using above formula

Sum = pow (((Number * (Number + 1)) / 2), 2);
Sum = pow (((5 * (5 + 1)) / 2), 2);
Sum = pow (((5 * 6) / 2), 2);
Sum = pow ((30 / 2), 2);
Sum = pow (15, 2);
Sum = 15 * 15 = 225

Final printf statement will print the Sum as output

printf("\n The Sum of Series for %d = %d ",Number, Sum);
So the final output will be

The Sum of Series for 5 = 225

C Program to Find Sum of series 1³+2³+3³+….+n³ using For Loop

If you want to display the series order 1³+2³+3³+4³ in the output then we have to add extra For Loop to display as below

/* Sum of Cubes of n Natural Numbers */

#include <stdio.h>
#include <math.h>

int main()
{
  int Number, i, Sum = 0;

  printf("\nPlease Enter any positive integer \n");
  scanf("%d",&Number);

  Sum = pow(((Number * (Number + 1))/ 2), 2);
  
  for(i =1; i<=Number;i++)
  {
    if (i != Number)
       printf("%d^3 + ",i);
    
    else
       printf("%d^3 = %d ",i, Sum);
  }
}

OUTPUT

C Program to Find Sum of series 1³+2³+3³+....+n³ using for loop

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^3 + ",i);
    
    else
       printf(" %d^3 = %d ",i, Sum);
}
In the above screen shot user entered value is 4 So,

Sum = 100
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 1³+
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 1³+2³+3³+4³ = 100

C Program to Find Sum of series 1³+2³+3³+….+n³ 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 1³+2³+3³+….+n³ using FUNCTIONS.

/* Sum of Cubes of n Natural Numbers */

#include <stdio.h>
#include <math.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 = 0;
  Sum = pow (((Number * (Number + 1))/ 2), 2);;
  
  for(i =1;i<=Number;i++)
  {
   if (i != Number)
     printf("%d^3  + ",i);

   else
     printf(" %d^3 = %d ", i, Sum); 
  } 
}

OUTPUT

C Program to Find Sum of series 1³+2³+3³+....+n³ using functions

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 1³+2³+3³+….+n³ using Recursion

This C program allows the user to enter the value of N then, it will find the s sum of series 1³+2³+3³+….+n³ using RECURSION

/* Sum of Cubes of n Natural Numbers */

#include <stdio.h> 

int Sum_Of_Series(int);

int main()
{
  int Number, Sum;

  printf("\nPlease Enter any positive integer \n");
  scanf("%d",&Number);

  Sum =Sum_Of_Series(Number);

  printf("\nSum of the Series  = %d",Sum);
}

int Sum_Of_Series(int Number)
{
  if(Number == 0)
    return 0;
  
  else      
                         //Recursive Calling   
    return (Number * Number * Number) + Sum_Of_Series(Number-1);  
}

OUTPUT

C Program to Find Sum of series 1³+2³+3³+....+n³ using Recursion

ANALYSIS

int Sum_Of_Series(int);

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

Within the main() function,
We declared 2 integer variables Number and Sum. In the next line, we called the user defined function Sum_Of_Series() and assigned it to the integer variable Sum.
Sum = Sum_Of_Series(Number);
When the compiler reaches the function calling then it will jump to the function definition for the calculations.

Function Definition
Within the Sum_Of_Series (Number) function,
If the user entered Number is 0 then the function will return 0 else it will return

(Number * Number * Number) + Sum_Of_Series(Number-1);

Let us divide the above expression for better understanding
(Number * Number * Number) = Multiplying the number three times
Sum_Of_Series(Number-1) = Calling the same function with 1 number minus

From the above output, User entered value is 3,

Recursion 1
Number = 3 which is Greater than 0 and Sum is 0 so,
Sum = (Number * Number) + Sum_Of_Series(Number-1)
Sum = (3 * 3 * 3) + Sum_Of_Series (3 – 1)
Sum = 27 + Sum_Of_Series (2)
Sum value is = 27

Recursion 2
Number = 2 which is Greater than 0 and Sum is 27 so,
Sum = (Number * Number) + Sum_Of_Series (Number-1)
Sum = (2 * 2 * 2) + Sum_Of_Series (2 – 1)
Sum = 8 + Sum_Of_Series (1)
Sum value is: 27 + 8 = 35

Recursion 3
Number = 1 which is Greater than 0 and Sum is 35 so,
Sum = (Number * Number) + Sum_Of_Series (Number-1)
Sum = (1 * 1 * 1) + Sum_Of_Series (1 – 1)
Sum = 1 + Sum_Of_Series (0)
Sum value is: 35 + 1 = 36

Recursion 4
Number = 0 which means First if condition is True so it will exit from the function. Final value of Sum is 36.

NOTE: We must use some sort condition to exit the recursive calling. If you forgot the condition then the function will execute infinite times.

Thank you for Visiting Our Blog