Please do only (a).

2 Fun with induction (20 pts) Prove the following statements using induction: (a) (10 pts) i=0ni2=6n(n+1)(2n+1) for every non-negative integer n. (b) (10 pts) Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item priced at 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