# Where did this step come from? Problem on series converge/divergence.

1. Apr 14, 2013

### Lo.Lee.Ta.

1. The original problem is this, but I'm just trying to figure out this one particular step!

Ʃ n!/(nn)
n=1

2. I'm at this step:

lim ln(n/n+1)/(1/n) = lnp
n→∞

BUT THEN my teacher wrote out the next step, and I'm like, "What the heck is that?!"

This is the next step:

lim $\frac{\frac{1}{n/(n+1)}*\frac{(n+1)*1-n*1}{(n+1)^{2}}}{-1/n^{2}}$
n→∞

Aaaaaagh! What the heck is going on?!
How did he get to this step? O_O

I am stuck wondering how I am supposed to figure out the limit at: lim$\frac{ln(n/(n+1)}{1/n}$!

Thank you!

2. Apr 14, 2013

### drawar

He was applying the L'Hospital's Rule to a limit of indeterminate form 0/∞.

3. Apr 14, 2013

### SammyS

Staff Emeritus
$\displaystyle \lim_{n\to\,\infty} \left( \frac{\displaystyle \ln\left(\frac{n}{n+1}\right)}{\displaystyle \frac{1}{n}} \right)\ \$ is of the indeterminate form, 0/0 .

4. Apr 15, 2013

### drawar

Oops, sorry, just ignore what I've said.