SOLUTION: prove that. in a geometric series which has a sum to infinity. each term bears a constant ratio to the sum of all the following terms

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Question 982142: prove that. in a geometric series which has a sum to infinity. each term bears a constant ratio to the sum of all the following terms
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
prove that. in a geometric series which has a sum to infinity. each term bears a
constant ratio to the sum of all the following terms
We use  where "a" = the first term and r = the
common difference:

Suppose the series is 

The sum of all the terms following arn+1, using the formula is

.

We want to show that the ratio of the nth term  to the sum of all
the following terms  is a constant:

That ratio is found by dividing:

   =

   =

That simplifies to 

 r(1-r) which is a constant.

So we have proved the proposition.

Edwin
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