Help With a Power Series Problem

[fleet spruce]

Hello. So I was doing this question for practice, and I got the answer to be 2. However I have no idea whether that is correct or not, which is why I thought to ask the question in this server and compare answers. Any and all help is greatly appreciated. Thank you.

[quiet lily]

By 2, do you mean the radius of convergence? Or the interval itself?

[lime turret]

I also got 2 as radius of convergence

[fleet spruce]

Sorry yes the radius of convergence

But interval is 2<x<6 right?

[quiet lily]

Well it's correct.

[fleet spruce]

Thank you for your help. Is my interval correct as well? Just wondering

[quiet lily]

The bounds are correct but the inequality itself isn't.

[fleet spruce]

Oh yea I didn’t test the endpoints

[fleet spruce]

I got the the interval to include both 2 and 6

[quiet lily]

It doesn't include 6.

That is because; $\newline\sum_{n=1}^{\infty}\frac{1}{n}\newline$ which is the harmonic series, diverges and $\frac{1}{ln(x)}$ grows even faster.

[limber nymph]

0x

[fleet spruce]

I see thank you.

.solved