- #1
nille40
- 34
- 0
Hi all!
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
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