Determine the limit, if it exists, of the sequences whose nth term is given
a_n = (-1)^n * (n/(n+1))

Question

Determine the limit, if it exists, of the sequences whose nth term is given
a_n = (-1)^n * (n/(n+1))

anonymous · Answer

limit as $n\to \infty$ ?

anonymous · Answer

yes, i'm sorry if i left that out.

anonymous · Answer

I was thinking of taking the abs value and finding the limit, but upon doing that i get an answer of 1 which I know I cant use it if it does not equal 1.

anonymous · Answer

if you did not have that annoying $(-1)^n$ you would take 
$$\lim_{n\to \infty}\frac{n}{n+1}=1$$ but the term $(-1)^n$ makes it oscillate so no limit
goes to one and minus one

anonymous · Answer

*if it does not equal 0

anonymous · Answer

in other words it has two limits, which means it has no limit, but rather a lim inf and a lim sup

anonymous · Answer

so when doing a problem like this would I always take out the -1^n and evaluate ? even though the theorem says it would have to equal 0 for that limit to be the same ?

anonymous · Answer

nvm. I get it I missed the part where you say it oscillates. Thanks!