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Math Help - Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

  1. #1
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    Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

    Show that if n belongs to N, and:

    An: = (1 + 1/n)^n

    then An < An+1 for all natural n. (Hint, look at the ratios An+1/An, and use Bernoulli's inequality)

    I think i have a vague idea of what to do here, like im sure induction is involved in this proof/ However, im unsure how bernoullis inequality and the ratios help in the proof. Can anyone help me please?
    Last edited by habsfan31; September 29th 2010 at 12:35 PM. Reason: typo, its an < an+1
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  2. #2
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    made a mistake, that i fixed, it's supposed to be an < an+1 as opposed to the other way around.
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  3. #3
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    I started the problem by doing the ratios like it suggests and ended up with:

    [(1+1/(n+1))((1+1/(n+1)^n)]/(1+1/n^n) > 1

    Where do i go from here, and when do i use bernoullis inequality.
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