Question

Infinite Series -

Determine if the sequence converges or diverges. If it converges, state the limit.

\[a _{n} = (n/n+2)^n \]
\[\ln a_n = n*\ln(n/n+2) \]
\[\ln(n/n+2)/(1/n) \]
=1/(n+1)^2/(-1/x^2)
=-x^2/(x+1)^2

= lim n>infinity -2x/(2*(x+1)) = -1

ln an = -1
an = e^-1

Any thoughts? Correct, incorrect? Thanks!