Results 1 to 2 of 2

Math Help - Prove Sequence is Converges or diverge

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    47

    Prove Sequence is Converges or diverge

    Let {a_n} and {b_n} be two sequences and suppose that the set {n: (a_n) does not equal (b_n) is finite. Prove the sequences either both converge to the same limit or both diverge.

    I know the set is finite, so it contains a largest number N. How do the sequences compare for all n>N and prove
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by summerset353 View Post
    Let {a_n} and {b_n} be two sequences and suppose that the set {n: (a_n) does not equal (b_n) is finite. Prove the sequences either both converge to the same limit or both diverge.

    I know the set is finite, so it contains a largest number N. How do the sequences compare for all n>N and prove
    Let n_1,\cdots,n_m be the finite set of natural numbers such that a_{n_k}\ne b_{n_k} then we have that N\leqslant n\implies a_n=b_n where N=\max_{1\leqslant \ell\leqslant m}n_\ell. So...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove that the sequence converges.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 6th 2010, 06:48 AM
  2. prove that a sequence converges
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 1st 2010, 06:48 PM
  3. Prove this sequence converges
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 6th 2010, 12:18 PM
  4. Prove the tail of a sequence converges?
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 3rd 2010, 11:46 AM
  5. Replies: 2
    Last Post: August 28th 2009, 02:59 AM

Search Tags


/mathhelpforum @mathhelpforum