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To find the sum of this series, we will first analyze this series.

The series is:

The given series is 2,10, 30, 68…

**For example**

For n = 6 Sum = 464

On analysis of the given series, you will see that the series is the addition of two series first one is the series of n natural numbers and the second is the cube of n natural numbers this means the series can be split as:

2, 10 , 30 ,68 = (1+13) , (2+23), (3 + 33), ( 4 + 43)

so we can write the sum of the series as :

sum = 2 + 10 + 30 + 68… = ( 1 + 2 + 3 + 4...)+( 13 + 23 + 33 + 43….)

based on this the formula for calculation of the series will also be defined as the sum of formulas of the two.

the mathematical formula for finding the sum of the above series is :

n*(n + 1)/2 + (n*(n + 1)/2)^2

#include <stdio.h> int main() { int n = 6; int sum = (n*(n + 1)/2) + (n*(n+1)/2)*(n*(n+1)/2); printf("the sum of series till %d is %d", n,sum); return 0; }

the sum of series till 6 is 462

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