# Quick question about Ratio Test for Series Convergence

1. Apr 13, 2015

### ColtonCM

1. The problem statement, all variables and given/known data

This is the question I have (from a worksheet that is a practice for a quiz). Its a conceptual question (I guess). I understand how to solve ratio test problems.

"Is this test only sufficient, or is it an exact criterion for convergence?"

2. Relevant equations

Recall the ratio-test: If {an}n∈N is a positive sequence and there is a number a < 1 such that eventually an+1 ≤ a then the series is convergent. If, eventually, an+1 ≥ 1 then the series is divergent.

3. The attempt at a solution

I would assume that it would be considered "only sufficient," since if the result yields a ratio of one, convergence cannot be determined, thus it is not an absolute criterion.

Would this line of reasoning be correct?

Thanks,

Colton

2. Apr 13, 2015

### fourier jr

that sounds right. it's sufficient but not necessary because there are other ways to determine whether or not a series converges eg $\sum_{n} \frac{1}{n^{2}}$ is known to converge but the ratio test doesn't give any information about it.

3. Apr 13, 2015

### ColtonCM

Sounds good, thanks!