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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

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

n = 1 \sum \infty \frac{1}{7 n + 3}

n = 1 \sum \infty \frac{4 ^{n} + n}{n !}

n = 0 \sum \infty e^{- 0.2 n}

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

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