\(=\left(2012-1\right)\left(2012+1\right)-2012^2=2012^2-1-2012^2=-1\)
=(2012−1)(2012+1)−2012^2
=2012^2-1-2012^2
=-1
tìm x biết (x+2014)/2011 + (x+2013)/2012 = (x+2012)/2013 + (x+2011)/2014
Tính giá trị biểu thức :
\(A=\frac{\frac{1}{2013}+\frac{2}{2012}+\frac{3}{2011}+...+\frac{2011}{3}+\frac{2012}{2}+\frac{2013}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}}\)
cho a ,b,c thảo mãn a^2012+b^2012+c^2012=a^2013+b^2013+c^2013=1 tính B = a^2011+b^2012+c^2013
Tính giá trị biểu thức :
\(A=\frac{\frac{1}{2013}+\frac{2}{2012}+\frac{3}{2011}+...+\frac{2011}{3}+\frac{2012}{2}+\frac{2013}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}}\)
Giải phương trình 0,05(\(\left(\frac{2x-2}{2011}+\frac{2x}{2012}+\frac{2x+2}{2013}\right)=3,3-\left(\frac{x-1}{2011}+\frac{x}{2012}+\frac{x+1}{2013}\right)\)
bài 2 Tìm GTNN của biểu thức A=\(\text{x^2-5x+y^2+xy-4y+2012}\)
CM \(2011^{2013}+2013^{2011}\)chia hết cho 2012
\(\frac{\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2013}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2013}}{\frac{2012}{1}+2+\frac{2012}{2}+1+\frac{2011}{3}+1+...+\frac{1}{2013}+1-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{\frac{2014}{1}+\frac{2014}{2}+...+\frac{2014}{2013}-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2014\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-1\right)}\)
=\(\frac{1}{2014}\)
cho S= 2/(2012+1)+2^2/(2012^2+1)+2^3/(2012^2^2+1)+.....+2^(n+1)/(2012^2^n+1)+....+2^2013/(2012^2^2012+1).
So sanh S voi 2/2011
CMR:
a)122000-21000 chia hết cho 10
b)20112013+20132011 chia hết cho 2012
