**Sum of infinite GP series in c programming language**

#include<stdio.h>

int main(){

float a,r;

float sum=0;

printf("Enter
the first number of the G.P. series: ");

scanf("%f",&a);

printf("Enter
the common ratio of G.P. series: ");

scanf("%f",&r);

if(1 > r)

sum
= a/(1-r);

else

sum
= a/(r-1);

printf("\nSum of
the infinite G.P. series: %f",sum);

return 0;

}

**Sample output:**

Enter the first number of
the G.P. series: 1

Enter the common ratio of
G.P. series: .5

Sum of the infinite G.P. series:
2.000000

Enter the first number of
the G.P. series: 5

Enter the common ratio of
G.P. series: 2

Sum of the infinite G.P. series:
5.000000

**Definition of geometric progression (G.P.):**

A series of numbers in which
ratio of any two consecutive numbers is always a same number that is constant.
This constant is called as common ratio.

**Example of G.P. series:**

2 4 8 16 32 64

Here common difference is 2
since ratio any two consecutive numbers for example 32 / 16 or 64/32 is 2.

**Sum of G.P. series:**

S

_{n}=a(1–r^{n+1})/(1-r)**T**

_{n}term of G.P. series:
T

_{n}= ar^{n-1 }**Sum of infinite G.P. series:**

S

_{n}= a/(1-r) if 1 > r
= a/(r-1) if r > 1

6. Write a c program to find out the sum of given H.P.