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Show a sequence of amounts are a geometric series

  1. Aug 9, 2005 #1
    i am given a set of amounts R(1+i)^(n-1)+R(1+i)^(n-2)+...... R(1+i)^1,R and so on it has to do with compound interest.
    how do i prove this is a geometric series?
    Last edited: Aug 9, 2005
  2. jcsd
  3. Aug 9, 2005 #2

    look at the definition of a geometric series, and try to see how this example satisfies it.
  4. Aug 9, 2005 #3
    well i know that is satisfies it they are in the form of a geometric series but how do i show this? and actually PROVE it.
  5. Aug 9, 2005 #4


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    Well it's clear that the corresponding sequence [tex]R\left( {1 + i} \right)^0 ,R\left( {1 + i} \right)^1 ,R\left( {1 + i} \right)^2 , \ldots ,R\left( {1 + i} \right)^{n - 1} ,R\left( {1 + i} \right)^n[/tex] has the general term [tex]R\left( {1 + i} \right)^n[/tex].

    The ratio between two terms of the sequence is always [tex]\left( {1 + i} \right)[/tex], a constant, just what we need for a geometric sequence -> this gives of course a geometric series.
  6. Aug 9, 2005 #5
    yeah, it was actually a pretty straightforward question! you might have expected it to be harder than it was...
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