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:
I checked on pc an I believe it keeps being strictly increasing for the rest of the terms.
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!
Sorry guys you are right, my mistake!
It was when I wanted to check the behaviour of x^n/n on the pc and I was getting strange results(for example it started as decreasing and then became an increasing sequence).
It was this the very fact that convinced me I was going to need some help, forgetting that one should not apply things that are true for convergings sequences only.
Yes a useful question could be for what values it converges, that is answeared very clearly already! Thank you Zaratoustra!
My sincere apologies again,
Thank you guys!