Results 1 to 3 of 3

Math Help - Proof by induction

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    2

    Unhappy Proof by induction

    So, I do this at sixth form, but in further maths, so I guess it's closer to Uni maths than 'pre-college' work.

    I'm really stuck, I can't even work out my base step for this proof properly!

    Prove that the general term of the sequence described by
    U(n+1) = 3U(n) + 4, n E Z+
    is U(n) = 3^n - 2 n E Z+

    where u(1) = 1

    Normally, on the divisibility and series ones we've done, the base step is n=1, but I can't see how that's going to help me with this?!
    Last edited by thatsphatt; March 2nd 2010 at 05:17 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by thatsphatt View Post
    So, I do this at sixth form, but in further maths, so I guess it's closer to Uni maths than 'pre-college' work.

    I'm really stuck, I can't even work out my base step for this proof properly!

    Prove that the general term of the sequence described by
    U(n+1) = 3U(n) + 4, n E Z+
    is U(n) = 3^n - 2 n E Z+

    where u(1) = 1

    Normally, on the divisibility and series ones we've done, the base step is n=1, but I can't see how that's going to help me with this?!
    Hi thatsphatt,

    it seems that U(1)=1 is a missing piece of information.

    Then, using

    U_{n+1}=3U_n+4

    U_1=1

    U_2=3(1)+4=7=3^1-2

    U_3=3(7)+4=25=3^3-2

    U_4=3(25)+4=79=3^4-2

    and so on...

    Therefore

    F(k)

    U_{k}=3^k-2

    F(k+1)

    U_{k+1}=3^{k+1}-2

    3^{k+1}-2=(3)3^k-2=3\left(3^k-2\right)-2+6=3(U_k)+4

    This means the formulation being true for n=1 causes the formulation to be true for n=2,
    causing true for n=3, causing....... an infinite chain of cause and effect.

    Test for n=1

    U_2=3(1)+4=7

    U_2=3^2-2=9-2=7

    Therefore, the nth term, in terms of n only is

    U_n=3^n-2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    2
    Oh I see!
    I think I'll be able to write down what I need from that!
    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof by induction
    Posted in the Algebra Forum
    Replies: 13
    Last Post: January 31st 2011, 04:41 PM
  2. an induction proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: October 5th 2009, 01:31 PM
  3. proof by induction ...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 8th 2009, 02:07 PM
  4. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  5. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM

Search Tags


/mathhelpforum @mathhelpforum