Show a sequence of amounts are a geometric series

[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?

 

[Brad Barker]

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.

 

[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.

 

[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.

 

[Brad Barker]

yeah, it was actually a pretty straightforward question! you might have expected it to be harder than it was...