What is the sum from n=1 to infinity of (3^n)/(n^7) ?

The sum from n=1 to infinity of (3^n)/(n^7) is diverges

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sum from n=1 to infinity of (3^n)/(n^7)

n = 1 \sum \infty \frac{3 ^{n}}{n ^{7}}

diverges

Solution steps

n = 1 \sum \infty \frac{3 ^{n}}{n ^{7}}

Apply Series Ratio Test:

diverges

= diverges

n = 0 \sum \infty \frac{9}{π ^{n}}

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

k = 2 \sum \infty \frac{1}{( k - 1 ) ^{5}}

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

n = 0 \sum \infty \frac{9}{10}

What is the sum from n=1 to infinity of (3^n)/(n^7) ?
The sum from n=1 to infinity of (3^n)/(n^7) is diverges