5 Fun with Induction ots) Prove the following statements using induction: (a) (15 pts) ili+1) = n(n+1}{n+2) for every positive integer n. i=1 (b) (15 pts) Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item priced an integer number of dollars of value at least $8 can be paid for with these gift certificates without a need to use any other form of currency. For example, an item priced $16 can be paid with two $3 gift certificates and two $5 gift certificates