Question

Tìm x thuộc Q:   | x + 1,1 | + | x + 1,2 | + | x + 1,3 | + | x + 1, 4 | = 5

Cm :

1/2 + ( 1/2 )^2 + ( 1/2 )^3 +.....+ ( 1/ 2)^98 < 1

1/3 + 1/3^2 + 1/3^3 +.....+ 1/3^99 < 1/2

Answer 1

đặt B=1/3 + 1/3^2 + 1/3^3 +.....+ 1/3^99 

=>1/3B=1/3^2 + 1/3^3 +.....+ 1/3^100

=>1/3B-B=1/3^2 + 1/3^3 +.....+ 1/3^100-1/3-1/3^2-1/3^3-...-1/3^100

=>-2/3=1/3^100-1/3

=>B=(1/3^100-1/3):(-2/3)<1/2 (vì kết quả ra số âm )