(1-1/5)nhân(1-1/6)nhan(1-1/7)nhan(1-1/8)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
LT
1
LO
1
22 tháng 4 2018
\(=\frac{1}{5}\times\frac{1}{3}\times\frac{3}{7}\times\frac{1}{2}\)
\(=\left(\frac{1}{5}\times\frac{1}{2}\right)\times\left(\frac{1}{3}\times\frac{3}{7}\right)\)
\(=\frac{1}{10}\times\frac{1}{7}\)
\(=\frac{1}{70}\)
LT
2
13 tháng 8 2017
\(\frac{2}{5}:\frac{3}{7}x\frac{3}{7}:\frac{2}{5}+1999=\)\(\frac{2}{5}x\frac{7}{3}x\frac{3}{7}x\frac{5}{2}+1999=\)\(\left(\frac{2x7x3x5}{5x3x7x2}\right)+1999=\)\(1+1999=2000\)
\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)\)\(=\left(\frac{2}{2}-\frac{1}{2}\right)\)\(x\left(\frac{3}{3}-\frac{1}{3}\right)\)\(x\left(\frac{4}{4}-\frac{1}{4}\right)\)\(x\left(\frac{5}{5}-\frac{1}{5}\right)\)\(=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}=\)\(\frac{1x2x3x4}{2x3x4x5}=\frac{1x\left(2x3x4\right)}{\left(2x3x4\right)x5}=\frac{1}{5}\)\(.\)
13 tháng 8 2017
2/5:3/7 nhân 3/7:2/5+1999
=2/5 nhân 7/3 nhân 3/7nhân 5/2+1999
=14/15 nhân 15/14+1999
=1+1999
=2000
(1-1/2) nhân (1-1/3) nhân (1-1/4) nhân (1-1/5)
=1/2 nhân 2/3 nhân 3/4 nhân 4/5
=24/120
=1/5
TN
5
H
2
24 tháng 8 2019
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+..+\frac{1}{x\left(x+2\right)}=\frac{20}{41}\)
\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{20}{41}\)
\(1-\frac{1}{x+2}=\frac{20}{41}:\frac{1}{2}\)
\(1-\frac{1}{x+2}=\frac{40}{41}\)
\(\frac{1}{x+2}=1-\frac{40}{41}\)
\(\frac{1}{x+2}=\frac{1}{41}\)
\(x+2=41\)
\(x=41-2\)
\(x=39\)
XO
24 tháng 8 2019
Tìm x
a) \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{x\times\left(x+2\right)}=\frac{20}{41}\)
\(\Rightarrow\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+1\right)}\right)=\frac{20}{41}\)
\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{20}{41}:\frac{1}{2}\)
\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{40}{41}\)
\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{\left(x+2\right)}=\frac{40}{41}\)
\(\Rightarrow1-\frac{1}{x+2}=\frac{40}{41}\)
\(\Rightarrow\frac{1}{x+2}=1-\frac{40}{41}\)
\(\Rightarrow\frac{1}{x+2}=\frac{1}{41}\)
\(\Rightarrow x+2=41\)
\(\Rightarrow x=41-2\)
\(\Rightarrow x=39\)
Vậy x = 39
ta có :\(\left(1-\frac{1}{5}\right)x\left(1-\frac{1}{6}\right)x\left(1-\frac{1}{7}\right)x\left(1-\frac{1}{8}\right)\)
\(=\frac{4}{5}x\frac{5}{6}x\frac{6}{7}x\frac{7}{8}=\frac{4}{8}=\frac{1}{2}\)
\(\left(1-\frac{1}{5}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{7}\right).\left(1-\frac{1}{8}\right)\)
\(=\frac{4}{5}.\frac{5}{6}.\frac{6}{7}.\frac{7}{8}\)
\(=\frac{4}{8}\)
\(=\frac{1}{2}\)