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# quick convergence/divergence Q watch

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1. Does

diverge for any real value of s where there are 3 cases with s>0 s=0 and s<0?

2. It definitely diverges for s>1. After all, diverges, so something bigger than is eventually larger than 1/n on each interval is going to diverge as well, no? You could formalize this idea with the integral test. So you need to consider other cases than s>1.
3. oh yeah, cheers
also, if you integrate using the substitution
you get

and when s<-1 you get the second half of the evaluation divided by zero, does this mean the whole function diverges or is it undefined?

thanks a lot
4. (Original post by aerot85)
and when s<-1 you get the second half of the evaluation divided by zero, does this mean the whole function diverges or is it undefined?
When s<-1 you get (1/(s+1))*(ln(x))^a where a is negative so? And when s=-1 it is undefined.

Spoiler:
Show
It is undefined
5. yeah i thought that was the case, the question asked us to tell us for which ranges of s the integral converges, but as far as i could work out they all diverge. Thanks for your help.

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Updated: November 19, 2008
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