- #1
twoflower
- 368
- 0
Hi,
I really don't know which trick should I use to solve convergence of this sum:
[tex]
\sum_{n=1}^{\infty} a_{n}
[/tex]
where
[tex]
a_{n} = \left( 1 - \frac{1}{n^2} \right)^{n} - 1
[/tex]
Neither binomial development nor writing first few terms helped me, and because all terms of this sum are negative, I can't use many of theorems...
It seems it could have something to do with e, but I can't see the adjustment to get it exactly...
Thank you for any suggestion.
I really don't know which trick should I use to solve convergence of this sum:
[tex]
\sum_{n=1}^{\infty} a_{n}
[/tex]
where
[tex]
a_{n} = \left( 1 - \frac{1}{n^2} \right)^{n} - 1
[/tex]
Neither binomial development nor writing first few terms helped me, and because all terms of this sum are negative, I can't use many of theorems...
It seems it could have something to do with e, but I can't see the adjustment to get it exactly...
Thank you for any suggestion.