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Question #041d7

1 Answer

Dec 10, 2017

The series converges

Explanation:

Let #a_n=(1+1/n)^n/n^2#

The Cauchy's test is also called the root test.

#lim_(n->oo)root(n)|a_n|=lim_(n->oo)root(n)|(1+1/n)^n/n^2|#

#=lim_(n->oo)(1+1/n)/root(n)(n^2)#

#=0#

Therefore,

The series #a_n# converges by the root test as the limit is #<1#

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