jubateee

Answered

2022-01-07

Test the convergence of the following series:

$\frac{\sqrt{n+1}-1}{{(n+2)}^{3}-1}+\dots +\mathrm{\infty}$

Answer & Explanation

limacarp4

Expert

2022-01-08Added 39 answers

Since

$\frac{\sqrt{n+1}-1}{{(n+2)}^{3}-1}=\frac{1}{{n}^{\frac{5}{2}}}\frac{\sqrt{1+\frac{1}{n}}-\sqrt{\frac{1}{n}}}{{(1+\frac{2}{n})}^{3}-\frac{1}{{n}^{3}}}$

$\sim \frac{1}{{n}^{\frac{5}{2}}}$

your method looks fine.

your method looks fine.

Ethan Sanders

Expert

2022-01-09Added 35 answers

Using the p-test,

karton

Expert

2022-01-11Added 439 answers

It is clear that

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