/*************************************** 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 <iostream> using namespace std; int main() { // Get n from user int n; cout << "Please enter n: "; cin >> n; // Compute sum int sum = 0; for(int k = 0; k <= n; k++) { // compute numerator of n choose k int num = 1; for(int m = n; m > n - k; m--) num = num*m; // compute denominator of n choose k int den = 1; for(int i = 1; i <= k; i++) den = den*i; // add value of n choose k to sum sum = sum + num/den; } // Write value of sum cout << "Sum as k goes from 0 to " << n << " is " << sum << endl; return 0; }