program to get sum of 1+3/4+7/16+15/64..............................nth terms.

//program to get sum of 1+3/4+7/16+15/64..............................nth terms.
#include<stdio.h>

#include<conio.h>

void main()
{
   float i,n,k=2,sum=0,m=0;

   printf("enter  positive number for 'n'\n");
  scanf("%f",&n);

  for(i=1;i<=n;i++)
    {               

          sum=sum+(pow(k,i)-1)/(pow(k,m));

          m=m+2;    

     }

  printf("the sum=%f",sum);

getch();
}

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logics in mind:
->enter a number for range for which you want to get sum, say 'n'.

->let a variable 'sum' with initial value '0'

->we get sum using formula sum=sum+(pow(k,i)-1)/(pow(k,m)) because in terms 1+3/4+7/16+15/64...    ,

    ->we have two components namely numerator and denominator. Let's look at numerator;they are

           1,3,7,16.....it can be formulated as pow(k,i)-1 that is    2¹-1  .here the power goes on increasing
   ->similarly for denominator, it has power of 2 i.e.
                 2⁰,2²,2^{4. we can see here that power is increasing by 2.}

                for this we have,pow(k,m) then m=m+2
->we find sum inside loop

->at last we display the final sum.