I want to find the limit of the sequence:

$\displaystyle a_n=(-1)^n\frac{n}{n+1}$

$\displaystyle \lim_{n->\infty}a_n=\lim_{n->\infty}\mid (-1)^n \frac{n}{n+1} \mid $

$\displaystyle \lim_{n->\infty}\frac{n}{n+1}$

$\displaystyle =1$

My book says the sequence converges at -1.