1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical Induction using a strong hypothesis

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    If a0=1, and a1=2, and

    an=(a(n-1))^2/an-2 for n>=2,
    prove by induction that an=2^n for n>=0

    2. Relevant equations

    3. The attempt at a solution
    (B) a0=1=2^0=1 yes is true
    a1=2=2^1=2 yes is true

    (I) ak=(2k-1)^2/2k-2=2k

    Is it true that what I solved. It seems very easy.

    I started first with a(k+1)=(a(k+1-1))^2/a(k+1-2)=
    Please someone help if I am doing something wrong. I will appreciate. Thank you.
  2. jcsd
  3. Dec 4, 2008 #2
    It seems that you have the right idea, but I do not know what is different between (I) and your solution for ak+1. Where precisely is your inductive hypothesis?
  4. Dec 4, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    It IS very easy. So your induction step is: if a_{k-1}=2^(k-1) and a_{k-2}=2^(k-2) then a_k=2^(k) (by doing the algebra you doubtless did). It looks fine to me.
  5. Dec 4, 2008 #4
    That is where I am confused. I know that I need to fallow the form an=2^n

    Then I don't need to do a(k+1)....

    I did so many problems in my HW and now I don't get it what I am doing:smile:
  6. Dec 4, 2008 #5
    Thank you guys.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook