Use the ratio test to determine whether the series is convergent or divergent.

a) Convergent by ratio test

Step-by-step explanation:

Given is the series

General term =

To use ratio test

Let us write n+1 th term

=

Find ratio of n+1th term to nth term

We find that here numerator has degree as 1 and denominator as 3

SInce numerator has more powers, it approaches infinity faster than numerator thus making ratio tend to 0 as n becomes large

Since ratio tends to 0, we have this series is convergent.

step-by-step explanation:

just plug in each number for x and see which ones work and don't