What is the sum from n=1 to infinity of (10)/(n^3) ?

The sum from n=1 to infinity of (10)/(n^3) is converges

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sum from n=1 to infinity of (10)/(n^3)

n = 1 \sum \infty \frac{10}{n ^{3}}

converges

Solution steps

n = 1 \sum \infty \frac{10}{n ^{3}}

Apply the constant multiplication rule:

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

= 10 \cdot n = 1 \sum \infty \frac{1}{n ^{3}}

Apply p-Series Test:

converges

= 10 converges

= converges

n = 0 \sum \infty 5^{- 2 n + 1} 3 n

n = 0 \sum \infty ∣ sin (n) ∣

n = 1 \sum \infty \frac{2 n}{n + 2}

n = 1 \sum \infty \frac{2 n}{n ^{4} + 1}

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

What is the sum from n=1 to infinity of (10)/(n^3) ?
The sum from n=1 to infinity of (10)/(n^3) is converges