Ta có :
\(B=\dfrac{2009^{2010}-2}{2009^{2011}-2}< 1\)
\(\Leftrightarrow B< \dfrac{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\dfrac{2009^{2010}+2009}{2009^{2011}+2009}=\dfrac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}=\dfrac{2009^{2009}+1}{2009^{2010}+1}=A\)
\(\Leftrightarrow A>B\)
Chứng minh rằng:
Nếu \(\dfrac{a+2009}{a-2009}=\dfrac{b+2010}{b-2010}\) thì \(\dfrac{a}{2009}=\dfrac{b}{2010}\)
Tính: \(D=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2017}}{\dfrac{2011}{1}+\dfrac{2010}{2}+\dfrac{2009}{3}+...+\dfrac{1}{2011}}\)
Tìm x :
\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}+\dfrac{x-3}{2009}=\dfrac{x-4}{2008}\)
tìm x biết
\(\dfrac{x+4}{2008}+\dfrac{x+3}{2009}=\dfrac{x+2}{2010}+\dfrac{x+1}{2011}\)
B= \(\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2009}\). CM B>3
Tìm x biết:
a) x + 2x + 3x + 4x + ... + 2011x = 2012 . 2013
b)\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}-\dfrac{x-3}{2009}=\dfrac{x-44}{2008}\)
so sanh A=(192009+52009)2010 va B=(192010+52010)2009
1 cho x=2010.Tính giá trị của biểu thức A=\(X^{2010}-2009.x^{2009}-2009.x^{2007}-...-2009.x+1\)
cho 3 số a,b,c thỏa mãn \(\dfrac{a}{2009}=\dfrac{b}{2010}=\dfrac{c}{2011}\)
tính giá trị M= 4(a-b)(b-c)-(c-a)2
