You are here:

Advanced Math/Proof by Induction

Advertisement

Expert: - 12/14/2008


Question
Hi how would i prove by induction that n^2= asub(n-1) - asub(n-2)+ asub(n-3)+2(2n-3) for n greater than or equal to 4. asub1=1 asub2=4 asub3=9 I know you have to prove P(1) first. Then assume P(K) then P(k+1). If you plug 4 into n for P(1) it comes out 16=16. I do not understand how you would prove p(K+1). Thank You!

Answer
Assume P(n) holds true, then prove P(n+1) also holds true.

Since n^2 = (n-1)^2 - (n-2)^2 + (n-3)^2 + 2(2n-3)
If P(n+1) is also true, then
    (n+1)^2 = n^2 - (n-1)^2 + (n-2)^2 + 2(2n-1)
which reduces to (n+1)^2 = n^2 + 2n +1, a fact.
So P(n+1) is true when P(n) is true.

Hope this helps

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Chen Min

Expertise

All the conceptual questions, pure math & basic stats alike I am good at answering your algebra (including logarithm, functions, trigonometry) and geometry questions. I can also provide to you a firm understanding into basic calculus and other mathematical ideas and concepts. You can either ask questions in English or Chinese. Physics Qns that require rigorous math are also welcomed Important:Please avoid asking me questions related to economics.After all, I am only a secondary school student

Experience

A lot of participation in Math Olympiad Competition with numerous awards (Not always gold, though) CMO Gold, SMO Silver, SPhO Gold

Education/Credentials
So far, nothing.

©2012 About.com, a part of The New York Times Company. All rights reserved.