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Show a sequence of amounts are a geometric series

  • Thread starter yourmom98
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  • #1
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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?
 
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Answers and Replies

  • #2
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yourmom98 said:
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?

look at the definition of a geometric series, and try to see how this example satisfies it.
 
  • #3
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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.
 
  • #4
TD
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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.
 
  • #5
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yeah, it was actually a pretty straightforward question! you might have expected it to be harder than it was...
 

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