What is the sum from n=1 to infinity of n^5e^{n^3} ?

The sum from n=1 to infinity of n^5e^{n^3} is diverges

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sum from n=1 to infinity of n^5e^{n^3}

n = 1 \sum \infty n^{5} e^{n^{3}}

diverges

Solution steps

n = 1 \sum \infty n^{5} e^{n^{3}}

Apply Series Divergence Test:

diverges

= diverges

n = 2 \sum \infty (\frac{3}{5})^{2 n}

n = 1 \sum \infty \frac{- 1}{8 ^{n}}

n = 0 \sum \infty e^{- n^{8}}

n = 2 \sum \infty \frac{4}{n ^{3}}

n = 1 \sum \infty \frac{- 1 ^{n}}{n ^{3}}

What is the sum from n=1 to infinity of n^5e^{n^3} ?
The sum from n=1 to infinity of n^5e^{n^3} is diverges