[SOLVED] Use ratio test to determine if series converges or diverges

**vinson24** · April 23rd 2010, 06:50 PM

$\sum_{n=1}^{\infty}\ \frac{k!}{k^3}$
I'm stuck about half way through
this is what ive done so far
$lim_{k->\infty}\frac{(k+1)!}{(k+1)^3}*\frac{k^3}{k!}$
I know that getting rid of the factorials gives me k+1 in the numerator but im not sure how to simplify the $k^3$ and $(k+1)^3$

**chisigma** · April 23rd 2010, 07:05 PM

Is $\frac{(k+1)!}{(k+1)^{3}}\cdot \frac{k^{3}}{k!} = (k+1)\cdot (1-\frac{1}{k})^{3}$ so that...

Kind regards

$\chi$ $\sigma$

**Soroban** · April 23rd 2010, 07:11 PM

Hello, vinson24!

$\sum_{n=1}^{\infty}\ \frac{k!}{k^3}$

I'm stuck about half way through

This is what ive done so far: . $\lim_{k->\infty}\frac{(k+1)!}{(k+1)^3}\cdot\frac{k^3}{k! }$

I know that getting rid of the factorials gives me k+1 in the numerator
but im not sure how to simplify the $k^3$ and $(k+1)^3$

We have: . $\frac{(k+1)!}{k!}\cdot\frac{k^3}{(k+1)^3} \;=\;\frac{k+1}{1}\cdot\left(\frac{k}{k+1}\right)^ 3$

In the parentheses, divide top and bottom by $k\!:\quad \frac{k+1}{1}\cdot\left(\frac{1}{1+\frac{1}{k}}\ri ght)^3$

Got it?

**vinson24** · April 23rd 2010, 07:29 PM

yes diverges thanks

Thread: [SOLVED] Use ratio test to determine if series converges or diverges

LinkBack

Thread Tools

Display

[SOLVED] Use ratio test to determine if series converges or diverges

Similar Math Help Forum Discussions

Determine whether the integral converges or diverges

[SOLVED] Determine whether series converges or diverges

This problem is about a summation series...determine when it diverges or converges

determine of series converges or diverges

determine converges absolutely, conditonally or if diverges

Search Tags