What is the sum from n=1 to infinity of (8^n)/(n^k) ?

The sum from n=1 to infinity of (8^n)/(n^k) is diverges

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sum from n=1 to infinity of (8^n)/(n^k)

n = 1 \sum \infty \frac{8 ^{n}}{n ^{k}}

diverges

Solution steps

n = 1 \sum \infty \frac{8 ^{n}}{n ^{k}}

n \to \infty lim n \frac{\frac{8 ^{n}}{n ^{k}}}{\frac{8 ^{n + 1}}{( n + 1 ) ^{k}}} - 1 = - \infty

L < 1,

by the Raabe's test

= diverges

n = 1 \sum \infty sin^{n} (8)

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

n = 1 \sum \infty \frac{n !}{10 4 ^{n}}

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

n = 1 \sum \infty (- 0.6)^{n}

What is the sum from n=1 to infinity of (8^n)/(n^k) ?
The sum from n=1 to infinity of (8^n)/(n^k) is diverges