Question

Найдите сумму бесконечно-убывающей геометрической прогресии
7-21/4+63/16-189/64+...

Answer 1

$\displaystyle\bf\\b_{1} =7\\\\b_{2} =-\frac{21}{4} \\\\b_{2} =b_{1} \cdotq\\\\q=b_{2} :b_{1} =-\frac{21}{4} :7=-\frac{21}{4} \cdot\frac{1}{7} =-\frac{3}{4} \\\\\\S=\frac{b_{1} }{1-q} =\frac{7}{1-(-\frac{3}{4} )} =\frac{7}{1+\frac{3}{4} } =7:\frac{7}{4} =7\cdot\frac{4}{7} =4\\\\\\Otvet:S=4$