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Ok,I need to find the solution to this sequence: 1.(09), 1.(4), 2, 3, ?, 17

the number in parentesis is an infinite decimal like 1,099999 or in the second one 1,4444444,but i can't find an answer for that question. Source:http://zagaza.ru/za548.htm 1.(09), 1.(4), 2, 3, ?, 17

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  • $\begingroup$ Hint: try to write them as fractions? (Are you sure it's not 1.09090909) $\endgroup$ – deep thought Jan 10 at 0:35
  • $\begingroup$ yes i'm sure test creator told me that, you should see them as 1,09999 and 1,4444 but there could be another answer he said,so maybe you should see that as infinite decimal but as something else $\endgroup$ – alnesi Jan 10 at 0:49
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The first number must be $1.090909\dots$ because $1.09999\dots=1.1$

The solution:

$$\frac{12}{11},\frac{13}{9},\frac{14}{7},\frac{15}{5},\color{blue}{\frac{16}{3}},\frac{17}{1}$$

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