Chapter One: Homework1 : Page 26: 1.5, 1.12 1.5 Write a recursive method that returns the number of 1’ s in the binary representation of N. Use the fact that this is equal to the number of 1’ s in the representation of N/ 2, plus 1, if N is odd. #include <iostream> using namespace std; int rec(int n) { if (n==0) return 0; if((n%2)==0) return rec(n/2); else return 1+ rec(n/2); } int main() { int x=1; cout << rec(x) << endl; return 0; } 1.12 Prove the following formulas: 2 a. ∑𝑁 𝑖=1(2𝑖 − 1) = 𝑁 𝑁 3 2 b. ∑𝑁 𝑖=1 𝑖 = (∑𝑖=1 𝑖 )) https://math.stackexchange.com/questions/62171/proving -13-23-cdots-n3-leftfracnn12-right2-using-induct