Question

Fração geratriz = 2,02121...

Answer 1

$2_+ \frac{021-0}{990}= 2 + \frac{21}{990} =2+ \frac{7}{330}= \frac{(660+7)}{330}= \frac{667}{330}$

Seja x = 2,0212121... (multiplicando por 10)  

10x = 20,212121... (multiplicando por 1000)  (I)

1000x = 2021,212121...(II)

Subtraindo I de II

1000x - 10x = 2021 + 0,212121... -( 20 + 0,21,2121...)

990x = 2021 - 20 + 0,212121... - 0,212121...

990x = 2001

x = 2001/990 (simplificando por 3)

x = 667/330