convergence

Consider the two series, $S_A$ and $S_B$, where $S_A = \sum_{n=1}^{\infty} \frac{n^2}{2^n}$ $S_B = 1 + \frac{1}{2} + \frac{1}{8} + \frac{1}{16} + \frac{1}{64} + \frac{1}{128} + \fr...

Consider the following series: (i) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $\sum_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum_{n=1}^{\infty} \frac{1}{n!}$ Choose the correct...

Consider the following series: (i) $\sum\limits_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $ \sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum\limits_{n=1}^{\infty} \frac{1}{n!...

Consider the following series : $$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$ For which of the following combinations of c, d values does this series converge?