The following series are geometric series or a sum of two geometric series.
Determine whether each series converges or not.
For the series which converge, enter the sum of the series. For the series which diverges enter "DIV" (without quotes).
(a) $\displaystyle \sum_{n=1}^{\infty} \frac{6^n}{5^n} =$ ,
(b) $\displaystyle \sum_{n=2}^{\infty} \frac{1}{2^n} =$ ,
(c) $\displaystyle \sum_{n=0}^{\infty} \frac{2^n}{8^{2n+1}} =$ ,
(d) $\displaystyle \sum_{n=5}^{\infty} \frac{5^n}{6^n} =$ ,
(e) $\displaystyle \sum_{n=1}^{\infty} \frac{8^n}{8^{n+4}} =$ ,
(f) $\displaystyle \sum_{n=1}^{\infty} \frac{5^n +2^n}{6^n} =$ .