What is the sum from n=1 to infinity of 2/(n^{10)} ?

The sum from n=1 to infinity of 2/(n^{10)} is converges

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sum from n=1 to infinity of 2/(n^{10)}

n = 1 \sum \infty \frac{2}{n ^{10}}

converges

Solution steps

n = 1 \sum \infty \frac{2}{n ^{10}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 2 \cdot n = 1 \sum \infty \frac{1}{n ^{10}}

Apply p-Series Test:

converges

= 2 converges

= converges

n = 0 \sum \infty \frac{n ^{6}}{n !}

n = 4 \sum \infty 6^{- n}

n = 0 \sum \infty n \cdot 2

n = 1 \sum \infty \frac{1}{3 n ^{5} + 7}

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

What is the sum from n=1 to infinity of 2/(n^{10)} ?
The sum from n=1 to infinity of 2/(n^{10)} is converges