Freeflows
Geometric Series Equality
Let $ x $ and $ y $ be real numbers such that $ -1 < x < y < 1 $. Let $ G $ be the sum of the infinite geometric series whose first term is $ x $ and whose common ratio is $ y, $ and let $ G' $ be the sum of the infinite geometric series whose first term is $ y $ and whose common ratio is $ x $. If $ G = G', $ find $ x + y $.
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$