Hi everyone,

Prove the following:

$\displaystyle \lim_{n \to \infty} (n+2)^2 sin(\frac{1}{n}) = \infty$

I must show that for each $\displaystyle M>0$ we can find $\displaystyle N$ such that $\displaystyle (n+2)^2 sin(\frac{1}{n})> M$ for every $\displaystyle n>N$.

Thing is that I can't figure out how to "get rid of" $\displaystyle sin(\frac{1}{n})$. Is $\displaystyle sin(\frac{1}{n})$ bigger than anything for every $\displaystyle n$?

Thanks!