Hey Stormey.
Have you come across the Integral Test for convergence? I would suggest looking into that with the appropriate substitution.
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!
Yes, chiro is right, the integral test works.
- Hollywood
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:
which diverges.
- Hollywood