Help with condensation test

i guys.

i need to determine if this serie converges:

this is what i've tried so far:

i use condensation test and got the following:

now, my question is this:

can i say that since: does not converge the the whole thing does'nt converge?

is there more elegant way to handle this horrible serie?

thanks in advanced!

Re: Help with condensation test

Hey Stormey.

Have you come across the Integral Test for convergence? I would suggest looking into that with the appropriate substitution.

Re: Help with condensation test

Yes, chiro is right, the integral test works.

- Hollywood

Here is a link to the condensation test: Cauchy condensation test - Wikipedia, the free encyclopedia

Re: Help with condensation test

hi, and thanks for the help.

we didn't learn the integral test yet, so i'm supposed to answer it without it, i guess...

Re: Help with condensation test

Maybe this condensation test will do it.

which converges if and only if the following series converges:

This is what you did in your original post. Now let's do the condensation test again. Our original series converges if and only if the following series converges:

We think this diverges, so we simplify by making it smaller. We have , so our new sum is greater than or equal to:

which diverges.

- Hollywood

Re: Help with condensation test

brilliant!

thank you very much Hollywood.

didn't know i can use this test twice like that. :)