Let

Prove converges and find its sum.

This shouldn't be too bad. Just a neat series.

I started with:

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- Jul 5th 2008, 03:15 PMgalactusprove convergence and find sum
Let

Prove converges and find its sum.

This shouldn't be too bad. Just a neat series.

I started with:

- Jul 5th 2008, 11:44 PMCaptainBlack
- Jul 6th 2008, 12:22 AMflyingsquirrel
- Jul 6th 2008, 07:04 AMgalactus
Well done to all who attempted.

Here is what I done.

Starting where I left off:

Now, for any integer , we get:

Therefore,

Now, if we let we can see that

converges, and it has the sum

Which, it would appear, is pretty much the same idea that Paul had. - Jul 6th 2008, 07:58 AMThePerfectHacker
See this.