Chapter 9, Problem 11RE

Find the general term of the sequence, starting with $n=1,$ determine whether the sequence converges, and if so find its limit.

$\begin{array}{l}\text{(a)}\frac{3}{2^2-1^2},\frac{4}{3^2-2^2},\frac{5}{4^2-3^2},\mathrm{...}\\ \text{(b)}\frac{1}{3},-\frac{2}{5},\frac{3}{7},-\frac{4}{9},\mathrm{...}\end{array}$