Results 1 to 3 of 3

Math Help - Accumulation Points

  1. #1
    Member
    Joined
    Jul 2011
    Posts
    80

    Accumulation Points

    I am trying to find the set of accumulation points of the subset of the real numbers.

    {(-1)^n*(1+1/n): n is an element of the natural numbers}

    I plugged in values for n to find a pattern and got the following results:
    n=1: -2
    n=2: 3/2
    n=3: -4/3
    n=4: 5/4
    n=5: -6/7
    n=6: 7/6
    n=7: -8/7
    n=8: 9/8

    The values are negative when n is odd and positive when n is even. They begin to accumulate around -1 and 1, but not every point is represented. Does that mean the set of accumulation points is the empty set?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,952
    Thanks
    1629

    Re: Accumulation Points

    I'm not sure what you mean by "not every point is represented" but how can you say "they begin to accumulate around -1 and 1" and suggest that there are no accumulation points? For all even n, the subsequence is (1+ 1/n) which obviously converges to 1. For all odd n, the subsequence is -(1+ 1/n) which obviously converges to -1. The set of accumulation points is {-1, 1}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2011
    Posts
    80

    Re: Accumulation Points

    I realized after I posted that I contradicted myself. However, by doing so, I understand why those are the accumulation points.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 1st 2012, 11:03 PM
  2. Accumulation points
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 23rd 2012, 08:36 AM
  3. accumulation points or limits points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 27th 2010, 02:20 AM
  4. accumulation points
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 19th 2009, 09:08 AM
  5. Replies: 3
    Last Post: January 11th 2009, 11:49 AM

Search Tags


/mathhelpforum @mathhelpforum