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Old 02-27-2013, 11:36 AM
BojanVujatovic BojanVujatovic is offline
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Default 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.
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Old 02-27-2013, 10:53 PM
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yaser yaser is offline
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Default Re: Problem 2.5 - Proof by induction

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Originally Posted by BojanVujatovic View Post
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.
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Old 02-28-2013, 03:13 PM
BojanVujatovic BojanVujatovic is offline
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Default Re: Problem 2.5 - Proof by induction

Oh I see now, thank you professor!
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Old 09-19-2015, 07:29 AM
sayan751 sayan751 is offline
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Default 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.
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Old 09-21-2015, 04:48 PM
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magdon magdon is offline
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Default 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).

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Originally Posted by sayan751 View Post
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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