What is the sum from n=1 to infinity of n^2e^{n^3} ?

The sum from n=1 to infinity of n^2e^{n^3} is diverges

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sum from n=1 to infinity of n^2e^{n^3}

n = 1 \sum \infty n^{2} e^{n^{3}}

diverges

Solution steps

n = 1 \sum \infty n^{2} e^{n^{3}}

Apply Series Ratio Test:

diverges

= diverges

(\frac{x + 2}{x - 2})^{2}

\int_{1}^{2} \frac{1}{x ^{4}} d x

x \to 7 lim (\frac{x}{( x - 7 ) ^{2}})

\int \frac{x}{( x + 1 ) ( x ^{2} + 1 )} d x

x \to 3 + lim (\frac{x + 2}{x - 3})

What is the sum from n=1 to infinity of n^2e^{n^3} ?
The sum from n=1 to infinity of n^2e^{n^3} is diverges