Register to reply

Reverse Induction?

by Char. Limit
Tags: induction, reverse
Share this thread:
Char. Limit
#1
Dec6-10, 12:54 PM
PF Gold
Char. Limit's Avatar
P: 1,945
1. The problem statement, all variables and given/known data
Say I had a problem like this:

Prove that the nth derivative of x*e^(x) is (x+n)*e^(x) for all integer n.

Can I use reverse induction to prove for negative n? For example...

Say I proved it for my base case, n=0. In this case, the proof is trivial.

Then I prove that if the nth derivative is (x+n)e^(x), then the (n+1)th derivative is (x+n+1)e^(x). (I didn't provide the proof because there's a similar homework problem here, and the proof is easy anyway.

Can I then use reverse induction to prove that if the nth derivative is (x+n)e^(x), then the (n-1)th derivative is (x+n-1)e^(x), thus extending this case to negative derivatives (i.e., integrals)?

Am I even making sense?
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
micromass
#2
Dec6-10, 05:02 PM
Mentor
micromass's Avatar
P: 18,099
Hmm, I'm not sure if this is correct. You do have to use reverse induction though. But isn't it easier to show "if it holds for -n, then it holds for -n-1". Or is this what you meant?
Char. Limit
#3
Dec6-10, 05:03 PM
PF Gold
Char. Limit's Avatar
P: 1,945
Quote Quote by micromass View Post
Hmm, I'm not sure if this is correct. You do have to use reverse induction though. But isn't it easier to show "if it holds for -n, then it holds for -n-1". Or is this what you meant?
Well, that would probably work too. EDIT: Since my base case is n=0, I don't see much of a difference.


Register to reply

Related Discussions
Java Reverse Engineering, Comp Sci, & Technology Homework 4
Is there some reverse of annihilation? Quantum Physics 7
Difference between Strong Induction and Mathematical Induction? Calculus & Beyond Homework 5
Reverse the number Programming & Computer Science 0
Reverse FFT Electrical Engineering 1