Tính nhanh 2/3 + 2/6 + 2/12 + 2/24 + 2/48 + 2/96 + 2/192 .Đây là bài nâng cao mọi người làm giúp mình nhé
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GW
2 tháng 9 2021
\(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+...+\frac{2}{192}.\)
\(=2\times\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{192}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{12}+...+\frac{1}{96}-\frac{1}{192}\right)\)
\(=2\times\left(1-\frac{1}{192}\right)\)
\(=2\times\frac{191}{192}=\frac{191}{68}\)
2 tháng 9 2021
\(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+...+\frac{2}{192}\)
\(=\frac{1}{3.1}+\frac{1}{3.2}+\frac{1}{3.2^2}+...+\frac{1}{3.2^6}\)
\(=\frac{1}{3}.\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\right)\)
\(=\frac{1}{3}.A\)với \(A=\frac{1}{1}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\)
\(\Rightarrow2A=2.\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\right)\)
\(\Rightarrow2A=2+\frac{1}{1}+\frac{1}{2}+...+\frac{1}{2^5}\)
\(\Rightarrow2A-A=\left(2+\frac{1}{1}+\frac{1}{2}+...+\frac{1}{2^5}\right)-\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\right)\)
\(\Rightarrow A=2-\frac{1}{2^6}=2-\frac{1}{64}=\frac{127}{64}\)
\(\Rightarrow\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+...+\frac{2}{192}=\frac{1}{3}.\frac{127}{64}=\frac{127}{192}\)
VK
2
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
\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\)
\(2A=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\)
\(2A-A=\frac{4}{3}-\frac{2}{192}\)
\(A=\frac{4}{3}-\frac{2}{192}=\frac{127}{96}\)
NH
6 tháng 7 2016
Đặt \(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}\)
\(\frac{1}{2}A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
\(\frac{1}{4}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}\)
\(\frac{1}{2}A-\frac{1}{4}A=\frac{1}{3}-\frac{1}{384}\)
\(\frac{1}{4}A=\frac{127}{384}\)
\(A=\frac{127}{384}.4=\frac{127}{96}\)
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
=\(\frac{64+32+16+8+4+2+1}{96}=\frac{127}{96}\)
28 tháng 6 2019
\(\frac{1999x1999}{1995x1995_{ }}=\frac{1999^2}{1995^2}=\left(\frac{1999}{1995}\right)^2\)\(>1^2\)\(=1\)
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`
NN
25 tháng 7 2016
\(2A=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}.\)
\(A=2A-A=\frac{4}{3}-\frac{2}{96}=\frac{63}{48}\)
\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)
\(=2\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)
\(=2\times\left(\dfrac{64+32+16+8+4+2+1}{192}\right)\)
\(=\dfrac{127}{96}\)
2/3+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
=\(\dfrac{64+32+16+8+4+2+1}{96}\)
=\(\dfrac{127}{96}\)