What is the sum from n=1 to infinity of (5^n)/(n^3) ?

The sum from n=1 to infinity of (5^n)/(n^3) is diverges

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sum from n=1 to infinity of (5^n)/(n^3)

n = 1 \sum \infty \frac{5 ^{n}}{n ^{3}}

diverges

Solution steps

n = 1 \sum \infty \frac{5 ^{n}}{n ^{3}}

Apply Series Ratio Test:

diverges

= diverges

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

k = 1 \sum \infty 1

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

n = 1 \sum \infty \frac{n}{5 n - 3}

n = 0 \sum \infty \frac{2}{3 n}

What is the sum from n=1 to infinity of (5^n)/(n^3) ?
The sum from n=1 to infinity of (5^n)/(n^3) is diverges