Originally Posted by

**Melsi** Hello,

I've spent many hours today investigating a sequence, I finally reduced it to **(x^n)/n** which is the smallest it gets, for obvious reasons.

**My observations for x=1.4:**

$\displaystyle \frac{(1.4)^{2}}{2}=0.97$

$\displaystyle \frac{(1.4)^{3}}{3}=0.91 (smaller)$

$\displaystyle \frac{(1.4)^{4}}{4}=0.96 (bigger)$

$\displaystyle \frac{(1.4)^{5}}{5}=1.07 $

*I checked on pc an I believe it keeps being strictly increasing for the rest of the terms.*

**My questions:**

1. Is this a wide know behaviour, **if so**, any reference to this category for studying further would be a great help.

2. How do I call this sequence, increasing or decreasing because it gets strictly increasing after some point.

3. I suspect it does not converge because the terms are aproaching infinity, am I right?

Thank you very much!