# Does the series converge or diverge?

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#oo#

#sum_(n=1)1/(n^(1+1/n)#

##### 1 Answer

It diverges, since it is asymptotically equivalent to

#### Explanation:

Let's use the comparison test. It goes like this: if you want to know if a series

where both

In this case, since

we may try to use

So, the two series behave the same. Sine

then your series diverges as well.