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NT
26 tháng 10 2023
\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\\ =\dfrac{128}{192}+\dfrac{64}{192}+\dfrac{32}{192}+\dfrac{16}{192}+\dfrac{8}{192}+\dfrac{4}{192}+\dfrac{2}{192}\\ =\dfrac{128+64+32+16+8+4+2}{192}\\ =\dfrac{254}{192}=\dfrac{127}{96}\)
GG
4
4 tháng 12 2016
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
=\(\frac{64+32+16+8+4+2+1}{96}=\frac{127}{96}\)
24 tháng 9 2021
127/96 nhé
nếu sai bạn sửa cho mình nhé
thank you
mình cảm ơn trước
NT
Nguyễn thành Đạt
CTVHS
3 tháng 2 2023
\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)
\(=2\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)
\(=2\times\left(\dfrac{64+32+16+8+4+2+1}{192}\right)\)
\(=\dfrac{127}{96}\)
6 tháng 2 2023
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
=\(\dfrac{64+32+16+8+4+2+1}{96}\)
=\(\dfrac{127}{96}\)
29 tháng 3 2023
Ta có:
\(S=\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}+\dfrac{2}{384}\\ =\dfrac{2}{3}+\dfrac{2}{2\times3}+\dfrac{2}{2\times6}+\dfrac{2}{2\times12}+\dfrac{2}{2\times24}+\dfrac{2}{2\times48}+\dfrac{2}{2\times96}+\dfrac{2}{2\times192}\\ =\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\\ \)
\(\dfrac{S}{2}=\dfrac{1}{2}\left(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}+\dfrac{2}{384}\right)\\ =\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}+\dfrac{1}{384}\)
\(S-\dfrac{S}{2}=\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}-\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}+\dfrac{1}{384}\right)\\ =\dfrac{2}{3}-\dfrac{1}{384}=\dfrac{2\times128-1}{384}\\ =\dfrac{85}{128}\\ \Rightarrow S=\dfrac{85}{128}\times2=\dfrac{85}{64}\)
29 tháng 3 2023
\(A=\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}+\dfrac{2}{384}\)
\(A.2=\dfrac{4}{3}+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)
\(A=A.2-A=\dfrac{4}{3}-\dfrac{2}{384}=\dfrac{127}{96}\)
28 tháng 6 2017
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)
14 tháng 8 2017
\(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{192}\)
\(=2\times\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{192}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{12}+...+\frac{1}{96}-\frac{1}{192}\right)\)
\(=2\times\left(1-\frac{1}{192}\right)\)
\(=2\times\frac{191}{192}\)
\(=\frac{382}{192}=\frac{191}{96}\)
