What is the sum from n=1 to infinity of 1/(n^{10)} ?

The sum from n=1 to infinity of 1/(n^{10)} is converges

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sum from n=1 to infinity of 1/(n^{10)}

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

converges

Solution steps

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

Apply p-Series Test:

converges

= converges

n = 1 \sum \infty cos (\frac{nπ}{2})

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

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

n = 1 \sum \infty \frac{1}{n ^{2} + 16}

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

What is the sum from n=1 to infinity of 1/(n^{10)} ?
The sum from n=1 to infinity of 1/(n^{10)} is converges