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Given are two infinite series

$\qquad P: \sum \frac{n^{2}+1}{n^{2}}$ 

$\qquad Q: \sum\left(1+\frac{1}{n}\right)^{-n}$

The correct choice is

  1. $\text{P}$ is convergent series; $\text{Q}$ is divergent series
  2. $\text{P}$ is divergent series; $\text{Q}$ is convergent series
  3. Both $\text{P}$ and $\mathrm{Q}$ are convergent series
  4. Both $\text{P}$ and $\text{Q}$ are divergent series

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