Question

Геометрический прогресс
a) b1+b2+b3=42
log2b1+log2b2+log2b3=9
Найти bn=?
б)Геометрический прогресс
Sn=2+3+5+9+…+(2^n-1+1)
Найти сумму

Answer 1

$left{begin{array}{c}b_1+b_2+b_3=42,\ log_2b_1+log_2b_2+log_2b_3=9,\b_2^2=b_1cdot b_3;end{array}right. left{begin{array}{c}b_1+b_2+b_3=42,\ log_2b_1cdot b_2cdot b_3=log_22^9,\b_2^2=b_1b_3;end{array}right. \ left{begin{array}{c}b_1+b_2+b_3=42,\ b_1b_2b_3=512,\b_2^2=b_1cdot b_3;end{array}right. left{begin{array}{c}b_1+b_2+b_3=42,\ b_1b_3=frac{512}{b_2},\b_2^3=512;end{array}right.$
$left{begin{array}{c} b_2=8, \ b_1+b_3=34,\ b_1b_3=64;end{array}right. left{begin{array}{c} b_2=8, \ b_3=34-b_1,\ b_1^2-34b_1+64=0;end{array}right.left{begin{array}{c} b_2=8, \ b_3=34-b_1,\ left [ {{b_1=2} atop {b_1=32;}} right. end{array}right. \ left [ {{ left{begin{array}{c} b_1=2, \ b_2=8,\ b_3=32;end{array}right.} atop {left{begin{array}{c} b_1=32, \ b_2=8,\ b_3=2.end{array}right.}} right.$