How do you determine whether the infinite sequence $a_{n} = \frac{2 n}{n + 1}$ $a_n=(2n)/(n+1)$ converges or diverges?

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Answer 1 · 2014-09-21T13:06:01

Let us evaluate

$lim_{n to infty}a_n=lim_{n to infty}{2n}/{n+1}$

$=lim_{n to infty}{2n}/{n+1}cdot{1/n}/{1/n}$

$=lim_{n to infty}2/{1+1/n}=2/{1+0}=2$

Hence, the sequence ${a_n}$ converges to $2$ .

How do you determine whether the infinite sequence a_n=(2n)/(n+1)an=2nn+1a_n=(2n)/(n+1) converges or diverges?