Results 1 to 4 of 4

Thread: a few true or false questions about sequences/series and convergence

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    5

    a few true or false questions about sequences/series and convergence

    hi y'all, i'm having some real trouble with these T or F problems. I've tried to do them myself, but i have no idea if my answers are right. I would appreciate if you could tell me what you think the answers are so i can compare them to my own. Thanks!


    a.) a sequence {a[subscript]n} only converges if
    lim[subscript]n->infiniti a[subscript]n = 0


    b.) if lim[subscraipt]n->infiniti (a[subscript]n / b[subscript]n) = 1 , where
    a[subscript]n and b[subscript]n are positive for all n , and
    [Epsilon]infinity,n=1 of b[subscript]n converges,
    then [Epsilon]infinity,n=1 of a[subscript]n also converges.


    c.) if lim[subscript]n->infiniti a[subscript]n = 0 ,
    then [Epsilon]infinity,n=0 of a[subscript]n converges.


    d.) If a series is absolutly convergent, then it is convergent.


    e.) if a series is conditionaly convergent, then the terms of a series can be arranged so that the sum of ther series is pi.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    and your answers are ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    5

    Red face

    ok, but like i said, i'm really uncertain about these, except problems a and d, which i at least have some idea of what i'm doing(ish).

    a.) true

    b.) true

    c.) true

    d.) true

    e.) true
    Last edited by enormousface; May 15th 2009 at 09:56 AM. Reason: i was wrong on A, and B, i think
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Pinkk's Avatar
    Joined
    Mar 2009
    From
    Uptown Manhattan, NY, USA
    Posts
    419
    a) is false. A sequence will converge if it has any limit $\displaystyle L$. The sequence will diverge if the limit does not exist or the limit tends to $\displaystyle \infty$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Some true and false questions!
    Posted in the Algebra Forum
    Replies: 6
    Last Post: Jul 10th 2010, 01:43 PM
  2. Convergence True or False Proof
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Apr 26th 2010, 05:38 PM
  3. True/False questions about sequences
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 3rd 2009, 11:17 PM
  4. Primitive sequences (true or false questions).
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Apr 13th 2009, 06:10 PM
  5. 3 true and false questions
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Dec 13th 2006, 08:33 AM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum