# Show a sequence of amounts are a geometric series

1. Aug 9, 2005

### yourmom98

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. Aug 9, 2005

look at the definition of a geometric series, and try to see how this example satisfies it.

3. Aug 9, 2005

### yourmom98

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. Aug 9, 2005

### TD

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

The ratio between two terms of the sequence is always $$\left( {1 + i} \right)$$, a constant, just what we need for a geometric sequence -> this gives of course a geometric series.

5. Aug 9, 2005