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

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

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

n = 1 \sum \infty \frac{1}{( 6 n ) ^{6}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{( 6 n ) ^{6}}

Simplify

\frac{1}{( 6 n ) ^{6}} : \frac{1}{46656 n ^{6}}

= n = 1 \sum \infty \frac{1}{46656 n ^{6}}

Apply the constant multiplication rule:

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

= \frac{1}{46656} \cdot n = 1 \sum \infty \frac{1}{n ^{6}}

Apply p-Series Test:

converges

= \frac{1}{46656} converges

= converges

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

n = 1 \sum \infty (- 1)^{n} + 1

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

n = 1 \sum \infty (\frac{7 π}{8})^{n}

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

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