What is the sum from n=2 to infinity of 5/(n^3) ?

The sum from n=2 to infinity of 5/(n^3) is converges

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sum from n=2 to infinity of 5/(n^3)

n = 2 \sum \infty \frac{5}{n ^{3}}

converges

Solution steps

n = 2 \sum \infty \frac{5}{n ^{3}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 2 \sum \infty \frac{1}{n ^{3}}

Apply p-Series Test:

converges

= 5 converges

= converges

n = 0 \sum \infty \frac{( 0.8 ) ^{n}}{7}

n = 1 \sum \infty (\frac{n}{2 n})^{n}

n = 1 \sum \infty \frac{2 n}{5 n - 1}

n = 0 \sum \infty \frac{- 1 ^{n}}{5 ^{n}}

n = 0 \sum \infty \frac{1}{3 ^{2 n + 1}}

What is the sum from n=2 to infinity of 5/(n^3) ?
The sum from n=2 to infinity of 5/(n^3) is converges