# Quickie Ratio Test question

1. Dec 11, 2005

### badtwistoffate

Have to find the radius of convergence and interval of convergence,
the series is (3^n x^n ) / (n+1)^2,
did the ratio test and found the radius of convergence to be the 1/3.
now for finding the interval of convergence I plug in -1/3 and 1/3 into x and find out if it converges or not

For 1/3, it converges due to p-series, 2>1.

But for -1/3 I know it converges but can see why? Any help here at this endpoint?

2. Dec 11, 2005

### shmoe

You could use the alternating series test.

More simply, you can relate the series at -1/3 to the series at 1/3...

3. Dec 11, 2005

### badtwistoffate

I dont quite understand, the alternating series only works when An+1< or = to An, and in that series it doesnt, because An is negative and An+1 is postivie?
Could you elaborate and how I would relate it to the series at 1/3?

4. Dec 11, 2005

### shmoe

Look at the alternating series test again, it's the absolute values of the terms that are decreasing (and going to zero) while the sign is alternating.

The series at 1/3 is the absolute values of the terms of the series at -1/3, i.e. you've already should that the series at -1/3 is absolutely convergent.

5. Dec 11, 2005

### badtwistoffate

iiiiiiiiiii...
my book doesnt say absolute value... so idk. I see what you mean if thats true. Why doesnt my book say that it says just that its decreasing or equal too...

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook