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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. $c= 1, d = – 2$