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\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)\left(1-\frac{1}{1010}\right)\left(1-\frac{1}{1011}\right)\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot\frac{1008}{1009}\cdot\frac{1009}{1010}\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)
\(=\frac{1006\cdot1007\cdot1008\cdot1009\cdot1010\cdot1011}{1007\cdot1008\cdot1009\cdot1010\cdot1011\cdot1012}=\frac{503}{506}\)
=\(\frac{1006}{1007}.\frac{1007}{1008}.....\frac{1011}{1012}\)
=\(\frac{1006}{1012}\)
=\(\frac{503}{506}\)
nếu sai sót mong mọi người sửa lỗi đúng thì ủng hộ
Ta có: \(\left(1-\frac{1}{1007}\right)\times\left(1-\frac{1}{1008}\right)\times...\times\left(1-\frac{1}{1011}\right)\times\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\times\frac{1007}{1008}\times...\times\frac{1010}{1011}\times\frac{1011}{1012}\)
\(=\frac{1006}{1012}=\frac{503}{506}\)
\(\left(1-\frac{1}{1007}\right)\cdot\left(1-\frac{1}{1008}\cdot\right)...\cdot\left(1-\frac{1}{1011}\right)\cdot\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot...\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)
\(=\frac{1006.1007\cdot..\cdot2010\cdot2011}{1007\cdot1008\cdot....\cdot1011.1012}\)
\(=\frac{1006}{1012}\)
\(=\frac{503}{506}\)
1-1/2+1/3-1/4+1/5-1/6+...+1/2011-1/2012 / 1006-1006/1007-1007/1008-1008/1009-...-2010/2011-2011/2012
ta có: \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{x}.\)
\(A=1+\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{x}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2.2}+...+\frac{1}{x:2}\)
\(\Rightarrow2A-A=2-\frac{1}{x}\)
\(A=2-\frac{1}{x}=\frac{4095}{2048}\)
=> 1/x = 1/2048
=> x = 2048 ( 2048 = 211 )