Determine whether the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5^n+6^n}{{10}^n}$ converges or diverges. If

it converges, find its sum.

Select the correct answer below and, if necessary, fill in the answer box

within your choice.

A$.$

The series converges because $\underset{n}{lim}\frac{5^n+6^n}{{10}^n}=0.$ The sum of the

series is

$($Simplify your answer.$)$

The series converges because it is the sum of two

B$.$ geometric series, each with The sum of the series is

$($Simplify your answer.$)$

C$.$ The series diverges because $\underset{n}{lim}\frac{5^n+6^n}{{10}^n}0$ or fails to exist.

D$.$

The series diverges because it is the sum of two

geometric series, at least one with $|r|1.$