Originally Posted by

**tonio** Try to add parentheses to make clear to others your expressions.

Let $\displaystyle \epsilon > 0$ be arbitrary. We want to show that for all but a finite number of indexes $\displaystyle n$ we have

$\displaystyle \mid\frac{n+5}{n^2+2}\mid<\epsilon$

As the expression between the absolute value is always positive we can drop the abs. value, so cross multiplying we get:

$\displaystyle n+5 <\epsilon n^2 + 2\epsilon \Longleftrightarrow \epsilon n^2-n+2\epsilon -5 >0$

Wel, now solve the quadratic inequality above and find your n!

Tonio