Results 1 to 7 of 7

Math Help - recurrence relations...

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    92

    recurrence relations...

    The questions read as follows:

    Find all solutions of the recurrence relation
    a -subscript-n = n+2-2a-subscript-n-1, a-subscript 1 = 0

    My instructor says it is similar to:
    Let R be the relation R-{(a,b) | a divides b} on the set of positive integers. Find
    A) r^-1
    B)R^-

    and

    Which of the relations from Example 7 are symmetric and which are antisymmetric?


    Do these indeed relate? I've read the entire chapter and haven't seen one problem setup like the one asked.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2009
    Posts
    92
    great! I see that my version of the book is the special indian edition so chapters are mixed up. Now Im only behind a chapter (being sarcastic!)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    92
    so far so good?
    Attached Thumbnails Attached Thumbnails recurrence relations...-equation.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Not quite.

     a_{n} = -2a_{n-1} + n + 2

    First find the solution to the homogeneous recursion

     a^{h}_{n} = -2a_{n-1}

    The characteristic equation of which is r+2=0, which has root r=-2 (multiplicity 1)

    so a^{h}_{n} = A (-2)^{n}

    Now we need a particular solution. For this problem we look for a solution of the form  a^{p}_{n} = Bn + C

    plugging it into the recursion we get  Bn + C = -2( B(n-1) + C)+ n + 2

     Bn + C = -2Bn + 2B - 2C + n + 2

    equating like terms we get

    B = -2B + 1
    C = 2B -2C + 2

    so B = 1 \over 3, and C = 8 \over 9

    so the general solution is  a^{h}_{n} + a^{p}_{n} = A(-2^{n}) + \frac {n}{3} + \frac {8}{9}

    If the problem had an intial condition, we could solve for A.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2009
    Posts
    92
    Quote Originally Posted by Random Variable View Post
    Not quite.

     a_{n} = -2a_{n-1} + n + 2

    First find the solution to the homogeneous recursion

     a^{h}_{n} = -2a_{n-1}

    The characteristic equation of which is r+2=0, which has root r=-2 (multiplicity 1)

    so a^{h}_{n} = A (-2)^{n}

    Now we need a particular solution. For this problem we look for a solution of the form  a^{p}_{n} = Bn + C

    plugging it into the recursion we get  Bn + C = -2( B(n-1) + C)+ n + 2

     Bn + C = -2Bn + 2B - 2C + n + 2

    equating like terms we get

    B = -2B + 1
    C = 2B -2C + 2

    so B = 1 \over 3, and C = 8 \over 9

    so the general solution is  a^{h}_{n} + a^{p}_{n} = A(-2^{n}) + \frac {n}{3} + \frac {8}{9}

    If the problem had an intial condition, we could solve for A.
    Wow, I was way off! Guess I just can't learn some things from the book
    Thanks for your assistance! Much appreciated.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    You can check that my answer (or any answer) is correct by plugging it into the recursion and seeing if both sides are equal.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Feb 2009
    Posts
    92
    Ill run a few variables through it. Thanks again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Recurrence Relations
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: July 28th 2011, 03:50 PM
  2. Recurrence relations
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: February 24th 2011, 10:45 AM
  3. Recurrence relations
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: December 1st 2010, 07:59 AM
  4. recurrence relations - degree of the recurrence
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 6th 2009, 08:56 PM
  5. recurrence relations
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 11th 2008, 12:57 AM

Search Tags


/mathhelpforum @mathhelpforum