Tính bằng cách hợp lí: (1-1/1007)*(1-1/1008)*(1-1/1009)*...*(1-1/1012)
K
Khách
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Những câu hỏi liên quan
16 tháng 10 2020
Ta có: \(\left(1-\frac{1}{1007}\right)\times\left(1-\frac{1}{1008}\right)\times...\times\left(1-\frac{1}{1011}\right)\times\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\times\frac{1007}{1008}\times...\times\frac{1010}{1011}\times\frac{1011}{1012}\)
\(=\frac{1006}{1012}=\frac{503}{506}\)
HT
16 tháng 10 2020
\(\left(1-\frac{1}{1007}\right)\cdot\left(1-\frac{1}{1008}\cdot\right)...\cdot\left(1-\frac{1}{1011}\right)\cdot\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot...\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)
\(=\frac{1006.1007\cdot..\cdot2010\cdot2011}{1007\cdot1008\cdot....\cdot1011.1012}\)
\(=\frac{1006}{1012}\)
\(=\frac{503}{506}\)
KN
0
NT
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
0
20 tháng 7 2017
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}+.....+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+........+\dfrac{x+2014}{1}\)\(\Leftrightarrow\left(\dfrac{x+1}{2014}+1\right)+\left(\dfrac{x+2}{2013}+1\right)+...+\left(\dfrac{x+1007}{1008}+1\right)=\left(\dfrac{x+1008}{1007}+1\right)+\left(\dfrac{x+1009}{1006}+1\right)+...+\left(\dfrac{x+2014}{1}+1\right)\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+1007}{1008}=\dfrac{x+2015}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+2015}{1008}-\dfrac{x+1008}{1007}-\dfrac{x+2015}{1006}-...-\dfrac{x+2015}{1}=0\)\(\Leftrightarrow\left(x+2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1\right)=0\)\(\Leftrightarrow x+2015=0\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1>0\right)\)\(\Leftrightarrow x=-2015\)
Vậy x=-2015
TH
0
NT
0
\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)\left(1-\frac{1}{1010}\right)\left(1-\frac{1}{1011}\right)\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot\frac{1008}{1009}\cdot\frac{1009}{1010}\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)
\(=\frac{1006\cdot1007\cdot1008\cdot1009\cdot1010\cdot1011}{1007\cdot1008\cdot1009\cdot1010\cdot1011\cdot1012}=\frac{503}{506}\)
=\(\frac{1006}{1007}.\frac{1007}{1008}.....\frac{1011}{1012}\)
=\(\frac{1006}{1012}\)
=\(\frac{503}{506}\)
nếu sai sót mong mọi người sửa lỗi đúng thì ủng hộ