Another real analysis problem.

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March 16th 2009, 07:15 AM
trojanlaxx223

Another real analysis problem.

prove the following:

lim (3n+1/n+2)=3
March 16th 2009, 07:35 AM
TheEmptySet

Quote:

Originally Posted by trojanlaxx223

prove the following:

lim (3n+1/n+2)=3

Let $\epsilon > 0$

Choose $N \in \mathbb{N}$ such that for all $n > N$

$n > \frac{5}{\epsilon} \iff \epsilon > \frac{5}{n}$

$\left| \frac{3n+1}{n+2}-3 \right|=\left| \frac{-5}{n+2}\right|< \frac{5}{n}< \epsilon$

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