For $n \geq1$, Let
$a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$
where$|c_{k}| \leq M$ for all integers $k$ and $|r| \leq 1.$ Then
(A) both $\{a_n\}$ and $\{b_n\}$ are Cauchy sequences
(B) $\{a_n\}$ is a Cauchy sequence but $\{b_n\}$ is not a Cauchy sequence
(C) $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence
(D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
