What is the sum from n=1 to infinity of 1/((4n+5)^3) ?

The sum from n=1 to infinity of 1/((4n+5)^3) is converges

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sum from n=1 to infinity of 1/((4n+5)^3)

n = 1 \sum \infty \frac{1}{( 4 n + 5 ) ^{3}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{( 4 n + 5 ) ^{3}}

Apply Series Comparison Test:

converges

= converges

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

n = 0 \sum \infty \frac{4}{2 ^{2 n - 2}}

k = 2 \sum \infty k e^{- 3 k^{2}}

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

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

What is the sum from n=1 to infinity of 1/((4n+5)^3) ?
The sum from n=1 to infinity of 1/((4n+5)^3) is converges