What is the sum from n=1 to infinity of (n^5)/(n^7) ?

The sum from n=1 to infinity of (n^5)/(n^7) is converges

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sum from n=1 to infinity of (n^5)/(n^7)

n = 1 \sum \infty \frac{n ^{5}}{n ^{7}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{5}}{n ^{7}}

Simplify

\frac{n ^{5}}{n ^{7}} : \frac{1}{n ^{2}}

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

Apply p-Series Test:

converges

= converges

n = 1 \sum \infty \frac{1}{ln ( 3 ^{n} )}

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

k = 2 \sum \infty k e^{- k^{2}}

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

n = 1 \sum \infty \frac{1}{n ln ^{2} ( n )}

What is the sum from n=1 to infinity of (n^5)/(n^7) ?
The sum from n=1 to infinity of (n^5)/(n^7) is converges