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

2/3+2/6+2/12+2/24+2/48+2/96+2/192=127/96

2/3+2/6+2/12+2/24+2/48+2/96+2/192=127/96

\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\\ =\dfrac{128}{192}+\dfrac{64}{192}+\dfrac{32}{192}+\dfrac{16}{192}+\dfrac{8}{192}+\dfrac{4}{192}+\dfrac{2}{192}\\ =\dfrac{128+64+32+16+8+4+2}{192}\\ =\dfrac{254}{192}=\dfrac{127}{96}\)