UGC-NET | UGC NET CS 2015 Dec – II | Question 11

Consider the following program :

#include <stdio.h>
main( )
{
    int i, inp;
    float x, term=1, sum=0; 
    scanf(“%d %f ”, & inp, &x);
    for(i=1; i<=inp; i++)
    {
      term = term * x/i; 
      sum = sum + term ;
    }
   printf(“Result = %f\n”, sum);
}

The program computes the sum of which of the following series?

(A) x + x²/2 + x³/3 + x⁴/4 +...
(B) x + x²/2! + x³/3! + x⁴/4! +...
(C) 1 + x²/2 + x³/3 + x⁴/4 +...
(D) 1 + x²/2! + x³/3! + x⁴/4! +...


Answer: (B)

Explanation: Fro i=1:
term = term * x / i = 1 * x / 1 = x.
sum = sum + term = x.
For i = 2:
term = x * x / 2 = x² / 2.
sum = x + x² / 2.
For i = 3:
term = x² / 2 * x / 3 = x³ / 3! .
sum = x + x² / 2 + x³ / 3!.
and so on...
So, option (B) is correct.


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