Đặt \(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}\)

\(\frac{1}{2}A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)

\(\frac{1}{4}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}\)

\(\frac{1}{2}A-\frac{1}{4}A=\frac{1}{3}-\frac{1}{384}\)

\(\frac{1}{4}A=\frac{127}{384}\)

\(A=\frac{127}{384}.4=\frac{127}{96}\)

khong ro moi hoi

2/3+2/6+2/12+2/24+2/48+2/96+2/192

=2/3+1/3+1/6+1/12+1/24+1/48+1/96

=\(\frac{64+32+16+8+4+2+1}{96}=\frac{127}{96}\)

Dễ lắm làm như này nè :I don't know

127/96 nhé bạn

127/96 nhé

nếu sai bạn sửa cho mình nhé

thank you 

mình cảm ơn trước

Bằng 127/96

\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\\ =1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{2}{192}\\ =\dfrac{5}{4}+\dfrac{7}{96}=\dfrac{127}{96}\)

\(A=\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{192}\)

=>\(2A=\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+...+\dfrac{2}{96}\)

=>\(2A-A=\dfrac{4}{3}-\dfrac{2}{192}\)

=>A=4/3-1/96=127/96

\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)

\(=2\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)

\(=2\times\left(\dfrac{64+32+16+8+4+2+1}{192}\right)\)

\(=\dfrac{127}{96}\)

=2/3+1/3+1/6+1/12+1/24+1/48+1/96

=\(\dfrac{127}{96}\)

127/96.Tích cho minh nha

\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)

= \(2\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)

= \(2\left(\dfrac{1}{1.3}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+\dfrac{1}{8.12}+\dfrac{1}{12.16}\right)\)

= \(\dfrac{2}{3}+2\left(\dfrac{1}{2}-\dfrac{1}{4}\right)+2\left(\dfrac{2}{4.6}+\dfrac{2}{6.8}\right):2+\dfrac{1}{2}\left(\dfrac{4}{8.12}+\dfrac{4}{12.16}\right)\)

= \(\dfrac{2}{3}+\dfrac{1}{2}+\dfrac{1}{8}+\dfrac{1}{32}\)

= \(\dfrac{127}{96}\)