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

  1. #1
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    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.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    and your answers are ?
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  3. #3
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    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
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  4. #4
    Senior Member Pinkk's Avatar
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    a) is false. A sequence will converge if it has any limit L. The sequence will diverge if the limit does not exist or the limit tends to \infty.
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