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Homework Help: How can I do this troglodyte of a series

  1. Dec 13, 2007 #1
    The series, which is by all accounts nefarious, is (-1)^(n)*n*e^(-2^n).

    In an attempt to subdue this monster, I made it into (-1)^(n)*n*/e^(2^n), but I do not want to wing the rest of the solution.

    So, I ask for your help. Help me, brothers, like there is no tomorrow.
     
  2. jcsd
  3. Dec 13, 2007 #2

    quasar987

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    Seems like a good candidate for Leibniz criterion of alternate series. If the general term in absolute value decrease and goes to zero, then the series converges.
     
  4. Dec 13, 2007 #3

    DaveC426913

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    BTW, troglodyte simply means underground dweller.
     
  5. Dec 13, 2007 #4
    Thanks, but I need to know why it converges absolutely, which is the case...
     
  6. Dec 13, 2007 #5

    quasar987

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    Can't you think of a convergence test you could apply on n*e^(-2^n) ?
     
  7. Dec 14, 2007 #6
    if tha absolute value converges...

    n/e^(2n), I would assume e grows faster since it is an exponential function...so the abs value converges?
     
  8. Dec 14, 2007 #7

    quasar987

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    That's an intuitive argument, not a mathematical proof.

    (And the argument is flawed too. For instance, for the series of 1/n. We have that 1/n-->0, but the series of 1/n still diverges.)
     
    Last edited: Dec 14, 2007
  9. Dec 14, 2007 #8
    Ok, so how else can I show that it is abs convergent? How should I demonstrate this?
     
  10. Dec 15, 2007 #9

    quasar987

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    There is a plethora of citerion to determine the convergence of a series. Have you tried them all?
     
  11. Dec 15, 2007 #10
    The vocabulary in this thread ROCKS!

    Casey
     
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