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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

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

n = 1 \sum \infty \frac{7 ^{n}}{n}

n = 1 \sum \infty [1 + (- 1)^{n}]

n = 1 \sum \infty \frac{4}{n ln ( n )}

n = 1 \sum \infty \frac{2}{n + 2}

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