00. This exercise is used in Sections 1.4, 2.4, and 5.1. Prove that the following formulas hold for all n EN.

(a) tk = n(n2+ 1).

k=l

(b) t k 2 = n(n + 1~(2n + 1).

k=l 2: n a-I 1

(c) -=1--, ak an k=l a ¥= O.

(d) t(2k _ 1)2 = n(4n~ -1).

k=l