Suppose you wish to use mathematical induction to prove that: 1. 1!+ 2· 2! +3· 3! +...+n•n! = (n +1)! - 1 for all n >= 1. a) Write P(1).

b) Write P(5). c) Write P(k). d) Write P(k + 1). e) Use mathematical induction to prove that P(n) is true for all n> 1.