Ta có :
\(\frac{2011}{-2012}\) = 2011 : ( -2012 ) = dương : âm = âm
\(\Rightarrow\) \(\frac{2011}{-2012}\) = âm
\(\frac{-2013}{-2012}\) = -2013 : ( -2012 ) = âm : âm = dương
\(\Rightarrow\) \(\frac{-2013}{-2012}\) = dương
Vì dương > âm
Nên \(\frac{-2013}{-2012}\) > \(\frac{2011}{-2012}\)
So sánh P và Q
\(P=\dfrac{2010}{2011}+\dfrac{2010}{2012}+\dfrac{2012}{2013};Q=\dfrac{2010+2011+2012}{2011+2012+2013}\)
so sánh A=2013^2010+1/2013^2011+1 và B=2013^2011-2/2013^2012-2
(1/2+1/3+..................+1/2012=1/2013).x=2012/1+2011/2+...................+2/2011+1/2012
(1/2+1/3+..................+1/2012=1/2013).x=2012/1+2011/2+...................+2/2011+1/2012
Tính: 2011+2012+2013/2012+2013+2014
Cho \(A=-\dfrac{10^{2011}+1}{10^{2012}+1}\) và \(B=-\dfrac{10^{2012}+1}{10^{2013}+1}.CMR:A< B\)
Tìm x biết:
a) \(^{2^x+2^{x+1}+2^{x+2}+2^{x+3}=480}\)
b) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{2}{2011}+\frac{1}{2012}\)
Tính \(\dfrac{P}{A}\)biết :
P=\(\dfrac{2013}{2}+\dfrac{2013}{3}+\dfrac{2013}{4}+...+\dfrac{2013}{2014}\)
A = \(\dfrac{2013}{1}+\dfrac{2012}{2}+\dfrac{2011}{1}+....+\dfrac{1}{2013}\)
cho A=1+2012+2012^2+2012^3+.......+2012^100 và B=2012^101/2011. Tính B-A