Question

Question #041d7

Answer 1

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`