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

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

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

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

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

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

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

Đặt bt bằng A

Ta có 2A= 2(2/3 + 2/6 + 2/12 +2/24 + 2/48 + 2/96 + 2/192)

2A= 4/3 +2/3 + 2/6 + 2/12 + 2/24 + 2/48 + 2/96

A= 2A-A= (4/3 +2/3 + 2/6 + 2/12 + 2/24 + 2/48 + 2/96) - (2/3 + 2/6 + 2/12 +2/24 + 2/48 + 2/96  2/192)

A=4/3 +2/3 + 2/6 + 2/12 + 2/24 + 2/48 + 2/96 - 2/3 - 2/6 - 2/12 - 2/24 - 2/48 - 2/96 - 2/192

A=(2/3 - 2/3) + (2/6 - 2/6) + ( 2/12 -  2/12) + (2/24 - 2/24) + (2/48 - 2/48) + ( 2/96 -  2/96) + (4/3 - 2/192)

A=0+0+0+0+0+0+ (256/192 - 2/192)

A=254/192

A=127/96(rút gọn phân số) 

\(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{192}\)

\(=2\times\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{192}\right)\)

\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{12}+...+\frac{1}{96}-\frac{1}{192}\right)\)

\(=2\times\left(1-\frac{1}{192}\right)\)

\(=2\times\frac{191}{192}\)

\(=\frac{382}{192}=\frac{191}{96}\)

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

\(=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)

\(=2.\left(1-\frac{1}{192}\right)\)

\(=2.\frac{191}{192}\)

\(=\frac{382}{192}=\frac{191}{96}\)

127/96 nhé

nếu sai bạn sửa cho mình nhé

thank you 

mình cảm ơn trước

Bằng 127/96

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

127/96.Tích cho minh nha

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

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

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

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

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

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

Đặt BT trên là A

\(2A=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}\)

\(A=2A-A=\frac{4}{3}-\frac{2}{192}=\frac{127}{192}\)

Sai