What is the sum from n=1 to infinity of (2^n)/(n^5) ?

The sum from n=1 to infinity of (2^n)/(n^5) is diverges

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sum from n=1 to infinity of (2^n)/(n^5)

n = 1 \sum \infty \frac{2 ^{n}}{n ^{5}}

diverges

Solution steps

n = 1 \sum \infty \frac{2 ^{n}}{n ^{5}}

Apply Series Ratio Test:

diverges

= diverges

n = 0 \sum \infty \frac{1}{7 n + 1}

n = 1 \sum \infty \frac{2}{3}

n = 0 \sum \infty \frac{1}{n 6 ^{n}}

k = 3 \sum \infty \frac{1}{k ^{2} + 5 k}

n = 1 \sum \infty \frac{9}{- 2 ^{n}}

What is the sum from n=1 to infinity of (2^n)/(n^5) ?
The sum from n=1 to infinity of (2^n)/(n^5) is diverges