Series Test for Convergence Problem

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?

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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.

jbunniii
Homework Helper
Gold Member
1. Is 1/(√(2n-1) convergent?
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.

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
1. Is 1/(√(2n-1) convergent?[/b]

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 comparison 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.[/b].

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?[/b]
(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.

I did not know I was not allowed to post using bold. I noticed the bold input letters were already there so just typed within them... I'm sorry I will not do it again.

Mark44
Mentor
Bolding removed. To the OP - please don't remove the parts of the template (problem statement, relevant equations, etc.). Removing these parts and then typing between the B tags caused everything you wrote to appear in bold.