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Alternating Series Test - No B_n?

  1. Jun 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Ʃ(-1/2)^k from 0 to infinity.

    2. Relevant equations

    Ʃ(-1)^k*B_n from 0 to infinity

    where if the series converges

    1. lim of B_n as n goes to infinity must = 0
    2. B_n must be decreasing

    3. The attempt at a solution

    It doesn't look like there is a B_n in the original equation at all. Do I manipulate it algebraically somehow to extract the B_n, or is there some clever trick?

    Is the B_n simply 1? If if that's the case, lim of 1 as n goes to infinity would just be one, but apparently that's not true from checking the answer (which is it does, indeed, converge).

    Thanks.
     
  2. jcsd
  3. Jun 25, 2013 #2

    HallsofIvy

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    Staff Emeritus
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    There quite obviously is a [itex]B_n[/itex].

    Your series is [itex]\sum (-1)^n(1/2)^n[/itex].
     
  4. Jun 25, 2013 #3



    I had to wrestle with my instinct that told me I'm not allowed to do that.. I guess I stand corrected.

    Thanks a lot, HallsofIvy.
     
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