A series is given by 1/4^1 + 2/4^2 + 3/4^3 + 4/4^4 + 5/4^5 +... .

Olivia correctly applies the ratio test to determine whether the series converges or diverges.

Which statement reflects Olivia's conclusion?

The general term is

In order to apply the ratio test, we have to compute the ratio between two consecutive terms:

The limit as of this ratio is

The ratio test states that if this ratio is between -1 and 1 (excluded), the series converges.

So, this series converges.

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)

a is the correct