What is the sum from n=1 to infinity of 1/((n+2)^3) ?

The sum from n=1 to infinity of 1/((n+2)^3) is converges

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sum from n=1 to infinity of 1/((n+2)^3)

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

k = 0 \sum \infty \frac{1}{100 + k}

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

n = 1 \sum \infty (- 1)^{n} n^{5}

n = 0 \sum \infty \frac{14}{14 + n}

k = 0 \sum \infty (- \frac{5}{8})^{k}

What is the sum from n=1 to infinity of 1/((n+2)^3) ?
The sum from n=1 to infinity of 1/((n+2)^3) is converges