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

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

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

k = 1 \sum \infty \frac{1}{( k - 1 ) ^{3}}

converges

Solution steps

k = 2 \sum \infty \frac{1}{( k - 1 ) ^{3}}

Apply Series Integral Test:

converges

= converges

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

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

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

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

n = 1 \sum \infty \frac{8 ^{n}}{n}

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