What is the sum from n=1 to infinity of (6^n)/(n^6) ?

The sum from n=1 to infinity of (6^n)/(n^6) is diverges

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sum from n=1 to infinity of (6^n)/(n^6)

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

n = 0 \sum \infty (1 + \frac{9}{n})^{n}

k = 1 \sum \infty \frac{k ^{4}}{k !}

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

n = 1 \sum \infty n^{- 5}

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

What is the sum from n=1 to infinity of (6^n)/(n^6) ?
The sum from n=1 to infinity of (6^n)/(n^6) is diverges