What is the sum from n=2 to infinity of 1/(n^5) ?

The sum from n=2 to infinity of 1/(n^5) is converges

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sum from n=2 to infinity of 1/(n^5)

n = 2 \sum \infty \frac{1}{n ^{5}}

converges

Solution steps

n = 2 \sum \infty \frac{1}{n ^{5}}

Apply p-Series Test:

converges

= converges

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

n = 0 \sum \infty \frac{3 n + 1}{2 n}

n = 1 \sum \infty \frac{1}{ln ( 4 ^{n} )}

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

n = 0 \sum \infty \frac{n ^{2}}{1 + 3 n}

What is the sum from n=2 to infinity of 1/(n^5) ?
The sum from n=2 to infinity of 1/(n^5) is converges