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The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if

  1. $a \in [-1, 1)$
  2. $a \in (-1, 1]$
  3. $a \in [-1, 1]$
  4. $a \in (-\infty, \infty)$
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