# Series Test for Convergence Problem

1. Oct 24, 2012

1. Is 1/(√(2n-1) convergent?

2. I have tried the first comparison test: an= 1/(√(2n-1) and bn=1/(n1/2. 0<=an<=bn. But bn diverges so we get no information.

I have tried the second comparson test and let bn=1/n. But an/bn=∞ so once again I get no information.

I have tried the ratio test but the limn→∞an+1/an=1 so I get no information.

I have tried the root test but limsupn→∞an=1 so I get no information..

3. I have run out of options! Can anyone offer a hint as to what I should try next? Perhaps a different bn for the first comparison test?

Last edited by a moderator: Oct 25, 2012
2. Oct 24, 2012

### gottfried

I'm busy doing my first course in real analysis at the moment so I'm no expert and could well be wrong but given than the sequence is decreasing you can and probably should use the integral test.

3. Oct 24, 2012

### jbunniii

I assume you mean
$$\sum_{n = 1}^\infty \frac{1}{\sqrt{2n-1}}$$
Note that $\sqrt{2n-1} \leq 2n-1 < 2n$. Try using this fact to apply the comparison test.

4. Oct 24, 2012

Sorry, I do mean the summation of 1/(√(2n-1)! Thank you very much for your help.

5. Oct 24, 2012

### SammyS

Staff Emeritus
(You may get a warning from a Moderator regarding posting in bold typeface.)

If the series diverges, then you need to compare your series to a divergent series which is smaller, term by term.

6. Oct 25, 2012