What is the sum from n=1 to infinity of 3/((2n+5)^3) ?

The sum from n=1 to infinity of 3/((2n+5)^3) is converges

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sum from n=1 to infinity of 3/((2n+5)^3)

n = 1 \sum \infty \frac{3}{( 2 n + 5 ) ^{3}}

converges

Solution steps

n = 1 \sum \infty \frac{3}{( 2 n + 5 ) ^{3}}

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

converges

= 3 converges

= converges

n = 1 \sum \infty \frac{3 n}{n ^{2} - 7}

n = 1 \sum \infty 2 e^{- 2 n}

n = 0 \sum \infty \frac{1}{1 - 4 n}

n = 1 \sum \infty \frac{9}{n ^{2} + 3 n}

n = 0 \sum \infty \frac{1}{n ^{- 2}}

What is the sum from n=1 to infinity of 3/((2n+5)^3) ?
The sum from n=1 to infinity of 3/((2n+5)^3) is converges