1. (a) Use the formulas s1 2 and snn-1+2 for all n22 to write a recursive algorithm that computes sn -2+4+6+..+2n (b) Use mathematical induction to prove that sumf hst e i-1 2 Determine whether each of the following statements is true or false. If the statement is true, prove it. If the statement is false, give a counterexample. (c) O If f(n)-O(h(n) and g(n)-0(h(n)), then f(n)+g(n) ( (ii) lg(n!)-O(nlgn)