LFD Book Forum Problem 2.5 - Proof by induction

#1
02-27-2013, 11:36 AM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
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.
#2
02-27-2013, 10:53 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Problem 2.5 - Proof by induction

Quote:
 Originally Posted by BojanVujatovic 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 (not just ) by inspection. Once you do that, the induction step will become easier.
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#3
02-28-2013, 03:13 PM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
Re: Problem 2.5 - Proof by induction

Oh I see now, thank you professor!
#4
09-19-2015, 07:29 AM
 sayan751 Junior Member Join Date: Jun 2015 Posts: 5
Re: Problem 2.5 - Proof by induction

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.
Attached Files
 2.5.pdf (55.5 KB, 201 views)
#5
09-21-2015, 04:48 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Problem 2.5 - Proof by induction

Your approach can work. To carry through your induction, you need an inequality like 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 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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