2.

(a) Show that (Sk2 + 2)/(4k2 - 1)2 < l/k2 for k = 2,3, ....

(b) Prove that for n E N.

(c) Prove that n 1 n-l (1 1) 1 L k2 ::; 1 + L k - k + 1 = 2 - n k=l k=l

{

2. 1

¢(x) = ~ SIllX- x~O x=O is of bounded variation on any bounded interval [a, b].