Question

Дано бн геометрическая прогрессия.б2=0,04 б4=0,16 Найти S9

Answer 1

$b_1, b_2=b_1q, b_3=b_2q =>q=frac{b_3}{b_2}=frac{0.16}{0.04}=4\\ b_1=frac{b_2}{q}=0.01;\ S_n=b_1frac{1-q^{n}}{1-q};=> S_9=b_1frac{1-q^{9}}{1-q}=0.01frac{1-4^{9}}{1-4}=\\ =0.01frac{1-262144}{-3}=0.01frac{-262143}{-3}=0.01cdot 87381=873.81$