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-   -   Problem 2.5 (http://book.caltech.edu/bookforum/showthread.php?t=4704)

 CountVonCount 10-25-2016 01:46 AM

Problem 2.5

Hello,

I tried to prove the unequally of problem 2.5 on page 69:

https://latex.codecogs.com/gif.latex...&plus;&space;1

However I was not able to find a good prove. I tried by using the same scheme like in the prove for

https://latex.codecogs.com/gif.latex...ce;=&space;2^N

But I had no success.

Can anyone give me the answer or at least a hint, how to start the prove well?

Thanks a lot,
André

P.S.: Is there a good way to embedd latex to this Forum? At the moment I just use https://www.codecogs.com for generating latex pictures.

P.P.S.: The book is very good and the course videos make a lot of fun to watch. Really: Thanks to everyone who worked on it!

 ntvy95 11-14-2016 08:18 PM

Re: Problem 2.5

I hope that I didn't make any mistake.

Base cases:

:
:
:

Induction step for :

I will prove later, for now, I will use its result:

:

:

So follows.

Quote:
 Prove:

 k_sze 03-16-2018 09:07 AM

Re: Problem 2.5

Quote:
 Originally Posted by ntvy95 (Post 12511)
Aside from the slight mistake in the product (it should be ), the whole proof is just amazing! How did you even come up this chain of logic and deduction?

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