What is the sum from n=1 to infinity of (e^n)/(n^4) ?

The sum from n=1 to infinity of (e^n)/(n^4) is diverges

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sum from n=1 to infinity of (e^n)/(n^4)

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

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

n = 5 \sum \infty cos (\frac{1}{n})

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

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

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

What is the sum from n=1 to infinity of (e^n)/(n^4) ?
The sum from n=1 to infinity of (e^n)/(n^4) is diverges