# Another Arithmetic series question.....

• June 12th 2009, 03:21 AM
anonymous_maths
Another Arithmetic series question.....
If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1)

Thanks for any help......
• June 12th 2009, 04:19 AM
mr fantastic
Quote:

Originally Posted by anonymous_maths
If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1)

Thanks for any help......

$S_{\infty} = \frac{a}{1 - r} \Rightarrow x = \frac{a}{1-r}$. Re-arrange to make $r$ the subject.

Substitute this expression for $r$ into the usual formula for $S_n$ and simplify.