Freeflows
Rational Function Generation
The function $ f(x) = x + 1 $ generates the sequence \[1, \ 2, \ 3, \ 4, \ \dots\]in the sense that plugging any number in the sequence into $ f(x) $ gives the next number in the sequence. What rational function $ g(x) $ generates the sequence \[\frac{1}{2}, \ \frac{2}{3}, \ \frac{3}{4}, \ \frac{4}{5}, \ \dots\]in this manner?
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$