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Prove a + ar + ar^2 + + ar^n < a/r - 1

  1. Jan 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that, if a>0 and 0<r<1, then for all n>=1 , a+ar+ar^2+...+ar^n < a/r -1

    2. Relevant equations

    3. The attempt at a solution

    could someone please give me some hints as to how to start this questions. thanks
  2. jcsd
  3. Jan 6, 2009 #2
    Re: Proof



    The series you have is a geometric progression, follow the derivation for the sum of a geometric progression on the wikipedia page. Once you have derived the sum take the limit as n goes to infinity.

    If this is a/(1 - r), or less, you have shown that the sum can never be greater than a/(1-r).

    To take the limit you will also need to explicitly show that the series converges for some range of r.
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