Question

Обчислити суму нескінченної геометричної прогресії:1/2; -1/6; 1/18; -1/54

Answer 1

$\displaystyle\bf\\b_{1} =\frac{1}{2} \\\\b_{2} =-\frac{1}{6} \\\\b_{2} =b_{1} \cdot q\\\\q=b_{2} :b_{1} =-\frac{1}{6} :\frac{1}{2} =-\frac{1}{6} \cdot 2=-\frac{1}{3} \\\\\\S=\frac{b_{1} }{1-q} =\frac{\dfrac{1}{2} }{1-\Big(-\dfrac{1}{3} \Big)} =\frac{\dfrac{1}{2} }{1+\dfrac{1}{3} } =\frac{\dfrac{1}{2} }{\dfrac{4}{3} } =\frac{1}{2} \cdot\frac{3}{4} =\frac{3}{8} =0,375\\\\\\Otvet: \ S=0,375$