Question

Найдите сумму бесконечной прогрессии,если b2-b4=1.5 и b1-b3=3

Answer 1

$b_2=b_1*q\\b_4=b_1*q^3\\b_3=b_1*q^2\\\left\{{{b_1*q-b_1*q^3=1.5}\atop{b_1-b_1*q^2=3}}\right.\\\left\{{{\frac{b_1*q-b_1*q^3}{b_1-b_1*q^2}=\frac{1.5}{3}}\atop{b_1-b_1*q^2=3}}\right.\\\left\{{{q=0.5}\atop{b_1=\frac{3}{1-0.25}}}\right.\left\{{{q=0.5}\atop{b_1=4}}\right.$

$S=\frac{b_1}{1-q}=\frac{4}{1-0.5}=8$