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I'm having a bit of difficulty with the following two problems:

The first asks to find the sum of the following series:

[tex]\sum\limits_{n = 1}^\infty {\frac{2}{n^2+4n+3}} [/tex]

I easily understand geometric series and how to find sums with those, but this seems a bit complicated. Factoring and pulling the 2 out doesn't seem to really help any. ...Any suggestions?

And this question:

Find a power series representation for the following:

[tex]g(x)=\arctan{\frac{x}{2}}[/tex]

I understand the simple 1/4+x^2 kind of stuff, but this I don't even know how to begin.

Any suggestions??

Thanks!

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# Homework Help: Find the sum of the following series

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