Question

Alguém pode me falar as funções geratrizes destas dízimas ? Obrigado desde já !

a) 0,111...
b) 5,020202...
c) 12,34222...
d) 2,777...
e) 1,710710710...
f) 0,1232323

Answer 1

$a)0,111...= \frac{1}{9}\\b)5,020202...5+ \frac{2}{99}= \frac{495+2}{99}= \frac{497}{99}\\c)12,34222...=12+ \frac{342-34}{900}= 12+\frac{308}{900}= \frac{10800+308}{900}= \frac{11108}{900}= \frac{2777}{225}\\d)2,777...=2+ \frac{7}{9}= \frac{18+7}{9}= \frac{25}{9}\\e)1,710710...=1+ \frac{710}{999}= \frac{999+710}{999}= \frac{1709}{999}\\f)0,1232323...= \frac{123-1}{990}= \frac{122}{990}= \frac{61}{495}$