Results 1 to 3 of 3

Math Help - Question about infinite sequences and series

  1. #1
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894

    Question about infinite sequences and series

    I'm studying the monotonic sequence theorem but can't really understand what it is used for? Does it just prove that a sequence converges but doesn't provide an answer to what it converges to? Can someone show me an example please? Also for the squeeze theorem how do you decide what sequence you use for A and C when B is between A and C? Thanks


    P.S. What is the bounded sum Test and how is it applied?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by 11rdc11 View Post
    I'm studying the monotonic sequence theorem but can't really understand what it is used for? Does it just prove that a sequence converges but doesn't provide an answer to what it converges to? Can someone show me an example please? Also for the squeeze theorem how do you decide what sequence you use for A and C when B is between A and C? Thanks
    The bounded monotone theorem says a sequence converges. Sometimes mathematicians only care if the sequence converges or diverges. They do not care what it converges to. Sometimes it can be really hard to find what it converges to. Thus, the theorem tells us something converges without the need to find the number.

    A stupid example would be a_n = \tfrac{1}{n}. This sequence is monotone (why?) and bounded (why?) thus it is convergent. In this case it is easy to see convergence.

    Here is an application of squeeze theorem. Say we want to find the limit of \tfrac{1}{n}\sin \tfrac{1}{n}. We note that -\tfrac{1}{n} \leq \tfrac{1}{n}\sin \tfrac{1}{n} \leq \tfrac{1}{n}. The outer sequences both converges to 0 thus the inner sequence converges to 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Thanks so its monotonic because it decreasing and seq a = 1/n and seq b = 1/(n +1) so seq of a is greater than seq b and since is bounded than seq a converges. Seq a converges to 0 because as the limit of n= infinity seq a equals 0. Is this right?

    Also rather than use squeeze theorem couldn't I always use hopital rule? Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite sequences and series?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 1st 2011, 04:18 PM
  2. infinite sequences and series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 29th 2009, 07:45 PM
  3. infinite sequences and series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 26th 2009, 07:04 PM
  4. Infinite Sequences & Series Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 6th 2009, 11:10 AM
  5. Infinite Sequences and Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 14th 2008, 02:28 PM

Search Tags


/mathhelpforum @mathhelpforum