Question

Запишите ряд,сумма которого равна числу: 0,(7)

Answer 1

$S_n= \frac{b_1}{1-q}=0.(7)= \frac{7}{9} = \frac{7}{9} =\frac{0.7}{0.9} \\\\ b_1=0.7 \\\ 1-q=0.9\rightarrow q=0.1 \\\ b_2=b_1q=0.7\cdot0.1=0.07 \\\ b_3=b_2q=0.07\cdot0.1=0.007 \\\\ (b_n):0.7;0.07;0.007;0.0007;...$