Could someone help me prooving the following:
for all natural numbers.
I hope that i have written everything correctly (this is my first time).
NB! How do i type in equations and stuff?
Thank you very much.
Please no double posting. On typing math symbols, see this thread for more: LaTex Tutorial
You can see the code that generates the image by clicking on it.
As for your problem, let's look at the inductive step. Assuming that , our goal is to prove that .
Looking at the LHS, notice that:
Now I highlighted the part in red for a reason .. and it shouldn't be too hard to show that this is bigger than .
Sorry for the inconvenience. The thing is that what you mentioned before is exactly what I have already done . . . and then I get stuck. I can't seem to get the "great idea" (maybe because I havn't slept all night).
What I'm trying to do is to reach the conslusion (instead of showing the truthfulness of an inequality):
Now from calculus I know that:
Using the inductive step we may write:
This is where I get stuck.
Your help is greatly appreciated.