Question

Arătați că nr a=2x[o,(3)+0,1(6)] este natural .

Answer 1

$a=2 \cdot [0,(3)+0,1(6)]= \\ ~~=2 \cdot ( \frac{3}{9}+ \frac{16-1}{90})= \\ ~~=2 \cdot ( \frac{1}{3}+ \frac{15}{90})= \\ ~~=2 \cdot ( \frac{1}{3}+ \frac{1}{6} )= \\ ~~= \frac{2}{3}+ \frac{1}{3}= \\ ~~=1 \in N$

Answer 2

a=2[3/9+15/90]
a=2[1/3+1/6]
a=2[2/6+1/6]
a=2·3/6⇒a=6/6⇒a=1⇒1∈N⇔a∈N⇔a-este natural;