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

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

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Answer 1 · 2015-03-04T17:53:23

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

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

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

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

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