Question

does this series converge or diverge?
n^(1/2)/(n+1)^3

Answer 1

if it is
\[\sum \frac{\sqrt{n}}{(n+1)^3}\] then it converges for sure

Answer 2

I think you can compare with sqrt(n)/n^3, can't you?

Answer 3

\[\sum_{n=1}^{\infty}\sqrt{n}/(n+1)^3\] explain!

Answer 4

if you wnant a precise reason, do what bmp said
if you want an easy quick eyeball answer the denominator has degree 3 and the numerator has degree \(\frac{1}{2}\) and \(3-\frac{1}{2}>1\) so it converges