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-   -   Problem 2.5 - Proof by induction (http://book.caltech.edu/bookforum/showthread.php?t=4039)

BojanVujatovic 02-27-2013 11:36 AM
Problem 2.5 - Proof by induction
 
I got stuck solving this problem. I know it is a simple proof by induction, but there is something I keep missing here. Has anybody tried to solve it? Any hints would be greatly appreciated.

yaser 02-27-2013 10:53 PM
Re: Problem 2.5 - Proof by induction
 
Quote:
Originally Posted by BojanVujatovic (Post 9571)
I got stuck solving this problem. I know it is a simple proof by induction, but there is something I keep missing here. Has anybody tried to solve it? Any hints would be greatly appreciated.
Take care of the small values of D (not just D=1) by inspection. Once you do that, the induction step will become easier.

BojanVujatovic 02-28-2013 03:13 PM
Re: Problem 2.5 - Proof by induction
 
Oh I see now, thank you professor!

sayan751 09-19-2015 07:29 AM
Re: Problem 2.5 - Proof by induction
 
1 Attachment(s)
Hi,
After seeing the reply from Prof. Mostafa, I have attempted to solve problem 2.5. I have also attached my solution with this reply.

However, I am not sure whether my approaches are right or not. It would be great if someone please validate my approaches. I know my approaches are naive, thus any pointer, how to improve this solution would be highly appreciated.

Thank You.

magdon 09-21-2015 04:48 PM
Re: Problem 2.5 - Proof by induction
 
Your approach can work. To carry through your induction, you need an inequality like N^D+DN^{D-1}\le (N+1)^D to allow you to connect the result after applying your induction hypothesis with what you are trying to prove.

You can also prove the result by induction on D, which is easier (instead of induction on N).

Quote:
Originally Posted by sayan751 (Post 12048)
Hi,
After seeing the reply from Prof. Mostafa, I have attempted to solve problem 2.5. I have also attached my solution with this reply.

However, I am not sure whether my approaches are right or not. It would be great if someone please validate my approaches. I know my approaches are naive, thus any pointer, how to improve this solution would be highly appreciated.

Thank You.


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