What is the sum from n=0 to infinity of 2/(n^3+5) ?

The sum from n=0 to infinity of 2/(n^3+5) is converges

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sum from n=0 to infinity of 2/(n^3+5)

n = 0 \sum \infty \frac{2}{n ^{3} + 5}

converges

Solution steps

n = 0 \sum \infty \frac{2}{n ^{3} + 5}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{1}{n ^{3} + 5}

Simplify

n^{3} : n^{2} n

= 2 \cdot n = 0 \sum \infty \frac{1}{n ^{2} n + 5}

Apply Series Comparison Test:

converges

= 2 converges

= converges

What is the sum from n=0 to infinity of 2/(n^3+5) ?
The sum from n=0 to infinity of 2/(n^3+5) is converges