Hi all!(adsbygoogle = window.adsbygoogle || []).push({});

I was wondering which method one should use to find the actual sum of an infinite series. I know how to find the sum of a geometric series (if it converges), but how could I find the sum for, for instance

[tex]

\sum_{n=0}^\infty\left(\frac{n+5}{5n+1}\right)^n

[/tex]

I know that it converges, and the sum appears to be 2. But how can I calculate this?

Or how about

[tex]

\sum_{n=0}^\infty\frac{\cos n\pi}{1+n^2}

[/tex]

Thanks in advance,

Nille

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# Infinite Series

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