Prove using induction that 1*1! + 2*2! + ....+n*n! = (n+1)! - 1 for any positive integer n.
a) What is the statement P(1)?
b) Show that P(1) is true, completing the base of the induction.
c) What is the inductive hypothesis?
d) What do you need to prove in the inductive step?
e) Complete the inductive step.