How do you determine if the summation #n^n/(3^(1+2n))# from 1 to infinity is convergent or divergent?

1 Answer
Massimiliano
Mar 4, 2015

The terms of this series are all positive, so the series is regular, that means that is divergent or convergent.
Since #n^n# is an infinite of higher order of #3^(1+2n)#,

#lim_(nrarr+oo)n^n/3^(1+2n)=+oo#,

the necessary condition (it has to be #0#) failed, so it is divergent.

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