What is the sum from n=1 to infinity of n^3e^{n^4} ?

The sum from n=1 to infinity of n^3e^{n^4} is diverges

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sum from n=1 to infinity of n^3e^{n^4}

n = 1 \sum \infty n^{3} e^{n^{4}}

diverges

Solution steps

n = 1 \sum \infty n^{3} e^{n^{4}}

Apply Series Ratio Test:

diverges

= diverges

n = 1 \sum \infty (- 1)^{n} \cdot n^{2}

n = 0 \sum \infty (3)^{n}

k = 1 \sum \infty \frac{7}{k} - \frac{7}{k + 1}

n = 1 \sum \infty \frac{3}{4 n ^{2} + 4 n}

k = 1 \sum \infty \frac{2 ^{k}}{k ^{3}}

What is the sum from n=1 to infinity of n^3e^{n^4} ?
The sum from n=1 to infinity of n^3e^{n^4} is diverges