Let $r = \frac{11}{22}.$
For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.

A. Consider the sequence $\lbrace n r^n \rbrace$.

$\displaystyle \lim_{n \rightarrow \infty} n r^n =$


B. Take my word for it that it can be shown that
$$\sum_{i=1}^{n} i r^i = \frac{n r^{n+2} - (n+1)r^{n+1} + r}{(1-r)^2} .$$

Now consider the series $\displaystyle \sum_{n=1}^{\infty} \, n r^n$.

$\displaystyle \sum_{n=1}^{\infty} \, n r^n =$