What is the sum from n=0 to infinity of (2^n)/(n^7) ?

The sum from n=0 to infinity of (2^n)/(n^7) is diverges

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sum from n=0 to infinity of (2^n)/(n^7)

n = 0 \sum \infty \frac{2 ^{n}}{n ^{7}}

diverges

Solution steps

n = 1 \sum \infty \frac{2 ^{n}}{n ^{7}}

Apply Series Ratio Test:

diverges

= diverges

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

n = 1 \sum \infty n! e^{- 4 n}

n = 1 \sum \infty \frac{8 n}{8 n + 1}

n = 0 \sum \infty \frac{1}{3 n - 1}

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

What is the sum from n=0 to infinity of (2^n)/(n^7) ?
The sum from n=0 to infinity of (2^n)/(n^7) is diverges