Originally Posted by
GrigOrig99 Q. Find in terms of x, in its simplest form, the sum of the infinite geometric series
x^2 + x^2/ (1 - x) + x^2/ (1 - x)^2 + x^2/ (1 - x)^3 +…
Eq.: S¥ = a/ 1 - r
Ans.: From text-book, x(x - 1)
Attempt: a = x^2, r = 1/ (1 - x)
x^2/ (1 - (1/ (1 - x)))
x^2(-1 + x) …. inverting 1/ (1 - x) and changing +/ - via the 1 - from 1 - 1/(1 - x)
x^3 - x^2
x^2(x - 1)
This is as close to the answer as I can get. I can’t quite work it out and was hoping someone could help. Thank you.