What is the sum from n=0 to infinity of 1/((n+1)^3) ?

The sum from n=0 to infinity of 1/((n+1)^3) is converges

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sum from n=0 to infinity of 1/((n+1)^3)

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty (\frac{8}{7})^{n}

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

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

n = 1 \sum \infty \frac{6}{3 n + 2}

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

What is the sum from n=0 to infinity of 1/((n+1)^3) ?
The sum from n=0 to infinity of 1/((n+1)^3) is converges