Have you come across the Integral Test for convergence? I would suggest looking into that with the appropriate substitution.
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!
Yes, chiro is right, the integral test works.
Here is a link to the condensation test: Cauchy condensation test - Wikipedia, the free encyclopedia
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: