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Consider the following series:

$$ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$$

For which of the following combinations of $c, d$ values does this series converge?

  1. $ c= 1, d = – 1$
  2. $ c= 2, d = 1$
  3. $ c= 0.5, d = – 10$
  4. $ c= 1, d = – 2$
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