S = d/dR [ R + R^2 + R^3 + R^4 + R^5 + ....... +R^n]

= d/dR [ R(R^n - 1 ]/[R-1]

= d/dR [R^(n+1) - R]/[R -1]

Using the Quotient Rule and simplifying:

S = [nR^(n+1) - (n+1)R^n + 1] / [R-1]^2

If n ----> infinity when -1<R<1, we get the long division infinite series you gave. So this is really just your solution in a different guise. But it can also be used for finite series when |R| >1

I'd really appreciate some help with this one, its got me stumped. I know the answer is 4, but don't know how to deal with the r in the numerator. Appreciate any help.

Brilliant, thanks very much

I'd really appreciate some help with this one, its got me stumped. I know the answer is 4, but don't know how to deal with the r in the numerator. Appreciate any help.