Alternating Series Calculus Help!!

Discussion in 'Undergraduate Math' started by Brian, Jan 9, 2011.

  1. Brian

    Brian Guest

    Is it possible for a series to converge without the constraint that a(sub.n+1)< or equal to a(sub.n)? Can we have a convergent series with only the requirement a(sub.n) >0 and the limit as x approaches infinity = 0 (i.e. not a decreasing monotonic series)?

    If yes include 3 series which disprove the conjecture stated, the math that shows these series diverge, how you came up with your 3 series and what makes your series diverge

    If no include the series to prove your conjecture, the math that shows your series converges, how you made your series and what makes your series converge
     
    Brian, Jan 9, 2011
    #1
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  2. On Sat, 08 Jan 2011 23:06:54 EST, Brian
    Yes, it is possible, but this looks too much like a homework
    question for me to be willing to go any further.

    [...]

    Brian
     
    Brian M. Scott, Jan 9, 2011
    #2
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  3. Brian

    Virgil Guest

    My take exactly!

    But hint:


    ANY finite series followed by a convergent series converges.
     
    Virgil, Jan 9, 2011
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