What is the sum from n=0 to infinity of 2/(n^3) ?

The sum from n=0 to infinity of 2/(n^3) is converges

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sum from n=0 to infinity of 2/(n^3)

n = 0 \sum \infty \frac{2}{n ^{3}}

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply p-Series Test:

converges

= 2 converges

= converges

n = 1 \sum \infty (\frac{4}{n})^{4}

n = 1 \sum \infty \frac{7}{n !}

n = 0 \sum \infty (\frac{7}{6})^{n}

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

k = 0 \sum \infty (\frac{1}{4})^{k}

What is the sum from n=0 to infinity of 2/(n^3) ?
The sum from n=0 to infinity of 2/(n^3) is converges