Question

Interval of convergence using ratio test?

Answer 1

The 2n+1 and 6n+3 parts are throwing me off a bit...\[\sum_{n=0}^{\infty} \frac{ (-1)^n*x ^{6n+3} }{ 2n+1 }\]

Answer 2

Please describe the interval test. \(\dfrac{a_{n+1}}{a_{n}}\)

It's just an algebra problem. How can it throw you off? Substitute carefully and use your best algebra!

Answer 3

I'm not sure if 2n+1 becomes 2n+3 ot 2n+2 when adding 1 to n for the ratio test, same for 6n+5... The rest I can do though

Answer 4

The algebra will tell you.

\(6n + 3 \rightarrow 6(n+1) + 3 = 6n + 6 + 3 = 6n + 9\)

You should not be struggling with this. Limits are enough to learn. Get your algebra up to speed. Let the notation help you!

Answer 5

Wherever you see "n" replace it with (n+1). Make sure you use the parenthesis.

Answer 6

That makes more sense. In class I was taught that 2n becomes 2n+2 because 2(n+1) but I wasn't aware n had to be replaced with (n+1). Thanks for pointing that out

Answer 7

I have a bit of learning impediment so I tend to be a bit slow until I fully understand, thanks for helping with clarification :)

Answer 8

You will do fine. Do it at your own pace when learning.