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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

converges

= 2 converges

= converges

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\int \frac{1}{x ln ( 2 )} d x

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