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For $n\geq 1$, let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ \dots +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + \dots + c_nr^n$,where $\mid c_k \mid  \leq M$ for all integer $k$ and $\mid r \mid  <1$. Then

  1. both $\{a_n\}$ and $\{b_n\}$ are Cauchy sequences
  2. $\{a_n\}$ is a Cauchy sequence,and $\{b_n\}$ is not Cauchy sequence
  3. $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence
  4. neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
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