1. ## Sequence question

Hi

A sequence is defined by
A = (-1)^n * [n/n+1]

What is the limit of the sequence? I know that this is an oscilating sequence (-1 and 1) but my teacher today told that its "LIMIT" was 0. I was not able to grasp the concept at all and somehow i dont trust my teacher too much.

can anyone help me out in this ?

thanks

2. $\lim_{n\to\infty}a_{2n}=\lim_{n\to\infty}\frac{2n} {2n+1}=1$

$\lim_{n\to\infty}a_{2n+1}=\lim_{n\to\infty}\left(-\frac{2n+1}{2n+2}\right)=-1$

So, the sequence $(a_n)$ has two subsequences that have different limits. Then $(a_n)$ has no limit.