Can someone please help me prove that this series is convergent? $ \sum_{i=1}^\infty \left({n^2+1\over n^2+n+1}\right)^{n^2} $
I guess I'm supposed to show that the limit of the sequence is an "e" limit, that means something of the kind: $ \left( 1\pm{1 \over a} \right)^a $ But how? I came to this state by now and that's where I'm stuck:
$ \left( {n^2+n+1-n \over {n^2+n+1}} \right)^{n^2} = \left( 1+{n \over {n^2+n+1}} \right)^{n^2} $