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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

n = 2 \sum \infty \frac{7}{5 ^{n}}

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

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

n = 1 \sum \infty \frac{9}{10}

n = 3 \sum \infty \frac{3}{n}

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