Question

Найдите сумму бесконечной геометрической прогрессии -4√2; 4; -2√2

Answer 1

$b_{1}=-4sqrt{2}\\b_{2}=4\\b_{2}=b_{1} *q\\q=frac{b_{2}}{b_{1}}=frac{4}{-4sqrt{2}}=-frac{1}{sqrt{2}}\\S=frac{b_{1}}{1-q}=frac{-4sqrt{2}}{1-frac{1}{sqrt{2}}}=-frac{4sqrt{2}}{frac{sqrt{2}-1}{sqrt{2}}}=-frac{4sqrt{2}*sqrt{2}}{sqrt{2}-1}=-frac{8}{sqrt{2}-1}=-frac{8*(sqrt{2}+1)}{(sqrt{2}-1)(sqrt{2}+1)}=-frac{8(sqrt{2}+1)}{2-1}=-8(sqrt{2}+1)$