Click here to download choosesum.c.

/***************************************
 Write a program that reads in a
 number n and prints out the sum
 as k goes from 0 to n of "n choose
 k".
              n*(n-1)*...*(n - k + 1)
 n choose k = -----------------------
                  k*(k-1)*...*2*1

 Note: If k is 0 then n choose k is 1.
 Note: If k is n then n choose k is 1.
****************************************/
#include "si204.h"

int main() {
  // Get n from user
  fputs("Please enter n: ", stdout);
  int n = readnum(stdin);

  // Compute sum
  int sum = 0;
  for(int k=0; k <= n; ++k) {
    // compute numerator of n choose k
    int numer = 1;
    for (int m = n; m > n-k; --m) {
      numer *= m;
    }

    // compute denominator of n choose k
    int denom = 1;
    for(int i=1; i <= k; ++i) {
      denom *= i;
    }

    // add value of n choose k to sum
    sum += numer / denom;
  }

  // Write value of sum
  fputs("Sum as k goes from 0 to ", stdout);
  writenum(n, stdout);
  fputs(" is ", stdout);
  writenum(sum, stdout);
  fputs("\n", stdout);

  return 0;
}