What is the sum from n=0 to infinity of 1/((2n+3)^3) ?

The sum from n=0 to infinity of 1/((2n+3)^3) is converges

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sum from n=0 to infinity of 1/((2n+3)^3)

n = 0 \sum \infty \frac{1}{( 2 n + 3 ) ^{3}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{( 2 n + 3 ) ^{3}}

(2 n + 3)^{3} = 8 n^{3} + 36 n^{2} + 54 n + 27

= n = 0 \sum \infty \frac{1}{8 n ^{3} + 36 n ^{2} + 54 n + 27}

Apply Series Comparison Test:

converges

= converges

f (x) = \frac{3}{11 - x}

\frac{\partial}{\partial y} (e^{4 y - x^{2} - y^{2}})

\frac{5}{x ^{4}} + 3 x^{2}

\frac{d}{d x} (\frac{2 x y}{x + y})

\frac{d}{d x} (154)

What is the sum from n=0 to infinity of 1/((2n+3)^3) ?
The sum from n=0 to infinity of 1/((2n+3)^3) is converges