\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}}{\left(\dfrac{2010}{2}+1\right)+\left(\dfrac{2009}{3}+1\right)+...+\left(\dfrac{1}{2011}+1\right)+1}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}}{\dfrac{2012}{2}+\dfrac{2012}{3}+...+\dfrac{2012}{2011}+\dfrac{2012}{2012}}=\dfrac{1}{2012}\)
Tính giá trị biểu thức:
\(D=\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}+\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}+\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}+\dfrac{2}{2004}}{\dfrac{2}{2002}+\dfrac{3}{2003}+\dfrac{3}{2004}}\)
\(H=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2012}}{\dfrac{2011}{1}+\dfrac{2010}{2}+...+\dfrac{1}{2011}}\)
\(I=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2012}}{\dfrac{2012}{2}+\dfrac{2012}{3}+...+\dfrac{2012}{2011}}\)
Help me!
Tính: \(D=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2017}}{\dfrac{2011}{1}+\dfrac{2010}{2}+\dfrac{2009}{3}+...+\dfrac{1}{2011}}\)
Rút gọn A=\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2013}}{2012+\dfrac{2012}{2}+\dfrac{2011}{3}+...+\dfrac{1}{2013}}\)
So sánh S và P biết:
S=\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2011}-\dfrac{1}{2012}+\dfrac{1}{2013}\)
P=\(\dfrac{1}{1007}+\dfrac{1}{1008}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\)
So sánh :
\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2011}}+\dfrac{1}{3^{2012}}\)và \(\dfrac{1}{2}\)
Cho S = \(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+.......+\dfrac{1}{2011}-\dfrac{1}{2012}+\dfrac{1}{2013}\)và P = \(\dfrac{1}{1007}+\dfrac{1}{1008}+....+\dfrac{1}{2012}+\dfrac{1}{2013}\). Tính\(\left(P-S\right)^{2013}\)
Tìm x biết:
a) x + 2x + 3x + 4x + ... + 2011x = 2012 . 2013
b)\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}-\dfrac{x-3}{2009}=\dfrac{x-44}{2008}\)
Tính B=\(\left(\dfrac{1}{2013^2}-1\right)\left(\dfrac{1}{2012^2}-1\right)\left(\dfrac{1}{2011^2}-1\right)....\left(\dfrac{1}{100^2-1}\right)\)
\(\dfrac{x+4}{2009}\)+\(\dfrac{x+3}{2010}\)=\(\dfrac{x+2}{2011}\)+\(\dfrac{x+1}{2012}\)
Tìm x, giúp mình với mn
