So, my homework says:
Find a value of $n \in\mathbb N$ from which there's certainty that:
...
c) $\frac{(-1)^n}{n+1}+2$ is within 1.9 and 2.1
I read this as "make sure that the limit is $2$, within a margin of $2.1 - 1.9$", which, turns into this:
$\left|\frac{(-1)^n}{n+1} +2 \right| < 2.1-1.9$
$(-1)^n < (\frac{1}{5}-2)(n+1)$
$(-1)^n < \frac{-9}{5}n - \frac{9}{5}$
$(-1)^n+\frac{9}{5}n<\frac{-9}{5}$
Now I'm stuck and don't know how to move on: assuming what I deduced is right, how am I supposed to get rid of that $(-1)^n$?