Q$10\mathrm{.}2\mathrm{.}2$B Determine whether the following series converges or diverges. If the series converges, then find its sum.

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{5^n}{2^{3n1}}$

the series converges; its sum is $10$

$(6)$ the series converges; its sum is $\frac{10}{3}$

$$ the series converges; its sum is $\frac{4}{3}$ the series converges; its sum is $\frac{5}{6}$ the series diverges