write a c program to find out the sum of infinite G.P. series | CTechnotips

#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–rⁿ⁺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