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May 1st, 2012, 05:59 PM   #1
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Series convergence

then after some integration lim (from b to infint) (-3/b+3)=1

so since the integration of 3/n^2 from one to infinity converges then the summation of infinity n=1 3/n^2 would converge?
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May 1st, 2012, 06:45 PM   #2
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Re: Series convergence

Yes.

We have

Now, since we may state:

If

then the series converges. So, we compute:



Hence, by the integral test, the series converges.
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May 1st, 2012, 06:55 PM   #3
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Re: Series convergence

YEY!
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May 1st, 2012, 07:13 PM   #4
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Re: Series convergence

Using the integral test, can you now determine for what values of x the following converges:

where
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