Ta có :
\(B=\frac{1011}{2012+2013}\)+\(\frac{2012}{2012+2013}\)=\(\frac{2011+2012}{2012+2013}\)
Vì:
\(\frac{2011}{2012+2013}\)<\(\frac{2011}{2012}\); \(\frac{2012}{2012+2013}< \frac{2012}{2013}\)
=> \(\frac{2011+2012}{2012+2013}< \frac{2011}{2012}+\frac{2012}{2013}\)
Mà \(\frac{2011+2012}{2012+2013}\)=B ; \(\frac{2011}{2012}+\frac{2012}{2013}\)
Vậy A <B
so sánh
A=\(\frac{2011+2012}{2012+2013}\) và B=\(\frac{2011}{2012}+\frac{2012}{2013}\)
bài 1: a)thực hiện phép tính :1-5-9+13+17-21-25+....+2001-2005-2009+2013
b)so sánh P và Q biết :
P = \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\) ; Q =\(\frac{2010+2011+2012}{2011+2012+2013}\)
So sánh:
A = \(\frac{2011^{2012}+1}{2011^{2013}+1}\)với B = \(\frac{2011^{2013}+1}{2011^{2014}+1}\)
So sánh A=2013^2010+1/2013^2011+1;B=2013^2011-2/2013^2012-2
so sánh
A= 2011 . 2013 và B= 20122
Bài 1: Tìm x, biết l) \(\left(x+1\right)\left(x+5\right)>0\) m) \(\frac{x+4}{2011}+\frac{x+3}{2012}+\frac{x+2}{2013}+\frac{x+1}{2014}=-4\)
\(\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\right).x=\dfrac{2012}{1}+\dfrac{2011}{2}+...\dfrac{1}{2012}\)
Rút gọn:
a) A= \(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2011}+\dfrac{1}{2012}}{\dfrac{2013}{1}+\dfrac{2014}{2}+...+\dfrac{4024}{2012}-2012}\)
Câu 1:
a) Cho S= \(\dfrac{1}{2}\)+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+............+\(\dfrac{1}{2^{2012}}+\dfrac{1}{2^{2013}}\). Chứng tỏ S<1
b) So Sánh: A=\(\dfrac{2011^{2012}+1}{2011^{2013}+1}\) với B=\(\dfrac{2011^{2013}+1}{2011^{2014}+1}\)
c) So Sánh: C=\(3^{210}\)với D=\(2^{310}\)
