Question

помогите, очень нужно)))

Answer 1

Ответ:

$a)1\frac{1}{9}$
б)$-\frac{1}{3}$
в)$4,8$
г)$2$

Пошаговое объяснение:

$a) 1;\frac{1}{10} ;\frac{1}{100};...;$
$b_1=1;b_2=\frac{1}{10};b_3=\frac{1}{100}$
$q=\frac{b_2}{b_1} =\frac{\frac{1}{10} }{1} =\frac{b_3}{b_2} =\frac{\frac{1}{100} }{\frac{1}{10} } =\frac{1}{10}; |q|=\frac{1}{10} < 1$
$S=\frac{b_1}{1-q}=\frac{1}{1-\frac{1}{10} }=\frac{1}{\frac{9}{10} }=\frac{10}{9}=1\frac{1}{9}$
б)$-\frac{1}{2};\frac{1}{4};-\frac{1}{6};...;$
$b_1=-\frac{1}{2}; b_2=\frac{1}{4}; b_3=-\frac{1}{6}$
$q=\frac{b_2}{b_1}=-\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{b_3}{b_2}=--\frac{\frac{1}{8}}{\frac{1}{4}}=-\frac{4}{8}=-\frac{1}{2}; |q|=\frac{1}{2} < 1$
$S=\frac{b_1}{1-q}=-\frac{\frac{1}{2}}{1+\frac{1}{2}}=-\frac{3}{2}=-\frac{1}{3}$
в)$6;-1\frac{1}{2};\frac{3}{8};...;$
$b_1=6;b_2=-1\frac{1}{2};b_3=\frac{3}{8}$
$q=\frac{b_2}{b_1} =-\frac{\frac{3}{2} }{6} =\frac{b_3}{b_2} =-\frac{\frac{3}{8} }{\frac{3}{2} } =-\frac{1}{4}; |q|=\frac{1}{4} < 1$
$S=\frac{b_1}{1-q}=\frac{6}{1+\frac{1}{4} }=\frac{6}{\frac{5}{4} }=\frac{24}{5}=4,8$
г)$\frac{2}{3};\frac{4}{9};\frac{8}{27};...;$
$b_1=\frac{2}{3};b_2=\frac{4}{9};b_3=\frac{8}{27}$
$q=\frac{b_2}{b_1} =\frac{\frac{4}{9} }{\frac{2}{3}} =\frac{b_3}{b_2} =\frac{\frac{8}{27} }{\frac{4}{9} } =\frac{2}{3}; |q|=\frac{2}{3} < 1$
$S=\frac{b_1}{1-q}=\frac{\frac{2}{3}}{1-\frac{2}{3} }=\frac{6}{\frac{5}{4} }=\frac{6}{3}=2$