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6 tháng 7 2016

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

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

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

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

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

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

6 tháng 7 2016

khong ro moi hoi

7 tháng 1 2023

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

16 tháng 8 2017

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

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

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

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

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

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

3 tháng 10 2020

Đặt BT trên là A

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

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

27 tháng 4 2021

Sai

3 tháng 11 2018

Đặt \(A=\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{98}+\dfrac{2}{192}\)

\(2A=\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{98}+\dfrac{2}{192}\)

\(2A-A=\left(\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{98}+\dfrac{2}{192}\right)-\left(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{98}+\dfrac{2}{192}\right)\)

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

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

Vậy \(A=\dfrac{127}{96}\)

3 tháng 11 2018

Mình hơn nhầm ở chỗ 98 viết lại thành 96. thông cảm nha mình làm lại cho:

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

\(2A=\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{96}+\dfrac{2}{192}\)

\(2A-A=\left(\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{96}+\dfrac{2}{192}\right)-\left(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\right)\)

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

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

Vậy \(A=\dfrac{127}{96}\)

27 tháng 8 2021

`a)-2/3-2/6+2/12+2/24+2/48+2/96+2/192`

`=-4/6-2/6+1/6+1/12+1/24+1/48+1/96`

`=-5/6+1/12+1/24+1/48+1/96`

`=-10/12+1/12+1/24+1/48+1/96`

`=-9/12+1/24+1/48+1/96`

`=-18/24+1/24+1/48+1/96`

`=-17/24+1/48+1/96`

`=-34/48+1/48+1/96`

`=-33/48+1/96`

`=-66/96+1/96=-65/96`

21 tháng 3 2016

+ 2/6 + 2/3 + 2/12 2/24 + 2/48 + 2/96 + 2/192 
= 2/3 x (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)  
Xét phần in Bracket: (1 +1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) 
1/2 + 1/4 = 1 1/4 - 
1/2 + 1/4 + 1/8 = 1 - 1/8 
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 1 - 1/64 = 63/64 
Suy ra 1 + 63/64 = 127/64 
2/3 + 2/6 + 2/12 + 2/24 + 2/48 + 2/96 + 2/192 
= 2/3 x 127/64 = 127/96

21 tháng 3 2016

127/96 h minh len 10 nha

5 tháng 8 2016

Đặt tổng trên = A

\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\)

\(A.2=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\)

\(A.2-A=\left(\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\right)-\left(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\right)\)

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

\(A=\frac{127}{96}\)

6 tháng 8 2016

\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\)

\(2A=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\)

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

\(A=\frac{4}{3}-\frac{2}{192}=\frac{127}{96}\)

25 tháng 7 2016

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

\(A=2A-A=\frac{4}{3}-\frac{2}{96}=\frac{63}{48}\)

3 tháng 7 2018

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

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

=\(2\)x (\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...\)\(+\frac{1}{48}-\frac{1}{96}\))

=\(2\)x (\(1-\frac{1}{96}\))

=\(2\)\(\frac{95}{96}\)

=\(\frac{190}{96}=\frac{95}{48}\)