Question

Consider the series. 16+24+36+54+...Does the series converge or diverge?

Answer 1

Step-by-step explanation

We are asked to determine if the given series converge or diverge

A series is said to be convergent when it approaches a certain value as the series approaches infinity.

To check, we will have this re-written as

`\sum _(n=0)^(\infty \:)16+24+36+54+\ldots \quad :\quad \sum _(n=0)^(\infty \:)-32\left(1-\left((3)/(2)\right)^n\right)`

Every infinite sum of a non-zero constant diverges

Therefore, the series diverges