What is the sum from n=1 to infinity of 2/(n^6) ?

The sum from n=1 to infinity of 2/(n^6) is converges

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sum from n=1 to infinity of 2/(n^6)

n = 1 \sum \infty \frac{2}{n ^{6}}

converges

Solution steps

n = 1 \sum \infty \frac{2}{n ^{6}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{n ^{6}}

Apply p-Series Test:

converges

= 2 converges

= converges

\int \frac{x ^{4} - 3 x ^{2} + 4 x}{5 x} d x

x \to \infty lim (\frac{e ^{x}}{1 - e ^{- x}})

x \to 1 + lim (\frac{3}{x ^{3} - 1})

- 9 e^{x^{- 9}}

\int \frac{1}{x ( ln ( 2 x ) )} d x

What is the sum from n=1 to infinity of 2/(n^6) ?
The sum from n=1 to infinity of 2/(n^6) is converges