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

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

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

k = 1 \sum \infty \frac{1}{k ^{3}}

converges

Solution steps

k = 1 \sum \infty \frac{1}{k ^{3}}

Apply p-Series Test:

converges

= converges

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

n = 2 \sum \infty (- 0.65)^{n}

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

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

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

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