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

1 Answer

Sep 21, 2014

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#.

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