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Math Help - Maximum values of the sequence

  1. #1
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    Maximum values of the sequence

    Hi
    If an = (1000^n )/ n! for n=1,2,3,..... then the sequence {an} :

    a. does not have a maximum
    b. attains maxima at exactly one value of n
    c. attains maxima at exactly two values of n
    d. attains maxima for infinitely many values of n

    thanks
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  2. #2
    Super Member Deadstar's Avatar
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    Use the ratio test to show it converges, ruling out a), since if it had no maxima it would diverge.
    EDIT - ignore what was here, think it was just rubbish, I cant give you a proof of why the answer is b), was getting a bit confused... Ask Mr F, he'll surely know.
    Just for your info, the series reaches a maxima at n=190 then starts to converge towards 0.
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  3. #3
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    actually the answer is C. that is why i was confused.
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