((picture) convergent and divergent series

This series is convergent

(A)

Step-by-step explanation:

We are given a series

Firstly, we will find nth term

So, numerator is

So, denominator is

so, nth term will be

now, we can use ratio test

Since, denominator has two n terms

so, we get

So, this series is convergent

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

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step-by-step explanation: