2014 - 1009 / 1008
cho
A=1/1008+1/1009+.....+1/2014
B=1/1008*2014+1/1009*2013+......+1/2014*1008
hay chung minh rang B/A la so nguyen
Tính B=1/1008*2014 + 1/1009*2013 + 1/1010*2012 + ...+ 1/2014*1008
B=1/1008 * 2004+1/1009*2004+...+1/2014*1008
A=1/1*2 + 1/3*4 + 1/5*6 + ... +1/2013*2014
B=1/1008*2014 + 1/1009*2013 + 1/1010*2012+ ... + 1/2014*1008
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
Cho:
A= 1/1*2+1/3*4+1/5*6+...+1/2013*2014
B=1/1008*2014+1/1009*2013+...+1/2014*1008
Tính A/B
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}=...+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}+.....+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+........+\dfrac{x+2014}{1}\)\(\Leftrightarrow\left(\dfrac{x+1}{2014}+1\right)+\left(\dfrac{x+2}{2013}+1\right)+...+\left(\dfrac{x+1007}{1008}+1\right)=\left(\dfrac{x+1008}{1007}+1\right)+\left(\dfrac{x+1009}{1006}+1\right)+...+\left(\dfrac{x+2014}{1}+1\right)\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+1007}{1008}=\dfrac{x+2015}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+2015}{1008}-\dfrac{x+1008}{1007}-\dfrac{x+2015}{1006}-...-\dfrac{x+2015}{1}=0\)\(\Leftrightarrow\left(x+2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1\right)=0\)\(\Leftrightarrow x+2015=0\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1>0\right)\)\(\Leftrightarrow x=-2015\)
Vậy x=-2015
1/1*2+1/3*2+1/5*6+.....+1/2013*2014
-------------------------------------------------------
1/1008*2014+1/1009*2013+1/1010*2012+....1/2014*2018
chứng minh: 1/1008x2014+1/1009x2013+....+1/2014x1008=1/1511x(1/1008+1/1009+...+1/2014)
(1/1008 + 1/1009 + 1/1010 +...+ 1/2014) : [1/2 + 1/(3.4) +1/(5.6) +...+ 1/(2013.2014)]=???