Results 1 to 2 of 2

Math Help - recurrence relations help

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    15

    recurrence relations help

    Solve the following recurrence relations:


    a) an=an-1+3(n-1), a0=1

    b) an=an-1+n(n-1), a0=3

    c) an=an-1+3n^2, a0=10

    d) an=2an-1+n, a0=1

    e) an=2an-1+2n2, a0=3

    I keep getting stuck quickly on each of these
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2008
    Posts
    80
    Hello,

    Here are some suggestions:
    Find f(n) such that b_n=a_n-f(n) has a nice property.

    a-c) a_n-f(n)=a_{n-1}-f(n-1)
    d) a_n-f(n)=2(a_{n-1}-f(n-1))

    I think we can find f(n) as a polynomial of n.
    For example,
    a) f(n)-f(n-1)=3(n-1). Let f(n)=pn^2+qn.
    By substituting, we see that p=3/2 and q=-3/2 works.
    Thus, b_n=b_{n-1}=b_0=1.
    a_n=f(n)+b_n=f(n)+b_0=(3/2)n^2-(3/2)n+1.

    e) I am not sure what you mean by "2n2",
    but the same method should work if this is "2n^2".

    a-c) It is also common to consider the sequence obtained by
    b_n=a_n-a_{n-1}.
    a_n=a_0+(b_1+b_2+...+b_n).
    For example,
    c)a_n=a_0+3(1^2+2^2+...+n^2)
    =10+3(1/6)n(n+1)(2n+1))=10+n(n+1)(2n+1)/2.

    I hope it helps.
    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, 02:50 PM
  2. Recurrence relations
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: February 24th 2011, 09:45 AM
  3. Recurrence relations
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: December 1st 2010, 06:59 AM
  4. recurrence relations - degree of the recurrence
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 6th 2009, 07:56 PM
  5. recurrence relations
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 10th 2008, 11:57 PM

Search Tags


/mathhelpforum @mathhelpforum