Question

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

Answer 1

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`.