What is the sum from n=1 to infinity of 3/(n^6) ?

The sum from n=1 to infinity of 3/(n^6) is converges

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sum from n=1 to infinity of 3/(n^6)

n = 1 \sum \infty \frac{3}{n ^{6}}

converges

Solution steps

n = 1 \sum \infty \frac{3}{n ^{6}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 1 \sum \infty \frac{1}{n ^{6}}

Apply p-Series Test:

converges

= 3 converges

= converges

\frac{d}{d x} (\frac{( x - 3 )}{x - 3})

x \to 0 lim (\frac{x ^{2} - 1}{x ^{2}})

\frac{3 x - 8}{x}

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{2})

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - \frac{29}{2}

What is the sum from n=1 to infinity of 3/(n^6) ?
The sum from n=1 to infinity of 3/(n^6) is converges