A=1-2+3-4+....+2011-2012+2013
Bài 1
so sanh 2010/2011+2011/2012+2012/2013+2013/2010 với 4
Bài 2
A=2011+2012/2012+2013 và B=2011/2012+2012/2013
Bài 3
E=1/3+2/32+3/33+..+100/3100
Chứng minh E<3/4
cho A=( 1/2+1/3+1/4+...+1/2013) / ( 2012+2012/2+2011/3+...+1/2013). Tim A
Rút gọn A= (1/2+ 1/3+ 1/4+.....+ 1/2013)/ ( 2012+ 2012/2 + 2011/ 3+....+ 1/ 2013)
Rút gọn A= (1/2+1/3+1/4+...+1/2013)/(2012+2012/2+2011/3+...+1/2013)
A = (2013/2 + 2013/3+2013/4 + ....+2013/2014) : (2013/1+2012/2 +2011/3+...+1/2013)
\(A=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(1+\frac{2012}{2}\right)+\left(1+\frac{2011}{3}\right)+...+\left(1+\frac{1}{2013}\right)+1}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{2014.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}\right)}\)
\(A=\frac{2013}{2014}\)
\(A=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(1+\frac{2012}{2}\right)+\left(1+\frac{2011}{3}\right)+...+\left(1+\frac{1}{2013}\right)+1}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{2014.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}\right)}\)
\(=\frac{2013}{2014}\)
TÍNH NHANH ;
A= 1*2+2*3+3*4+....+2011*2012
B =2012*2013+2013*2014
A=1/2+1/3+1/4+...+1/2014 phần 2013/1+2012/2+2011/3+...+1/2013
\(A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}}{\dfrac{2013}{1}+\dfrac{2012}{2}+...+\dfrac{1}{2013}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}}{\left(\dfrac{2012}{2}+1\right)+\left(\dfrac{2011}{3}+1\right)+...+\left(\dfrac{1}{2013}+1\right)+\dfrac{2014}{2014}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}}{2014\left(\dfrac{1}{2}+\dfrac{1}{.3}+...+\dfrac{1}{2014}\right)}\)
\(=\dfrac{1}{2014}\)
A=1/2+1/3+1/4+...+1/2014/2013/1+2012/2+2011/3+...+1/2013
(1/2+1/3+1/4+...+1/2013).x=2012/1+2011/2+...+2/2011+1/2012
mình đang cần gấp.Ngày 26 tháng 2 năm 2018 là mình phải nộp rồi
Tính giá trị biểu thức :
\(A=\frac{\frac{1}{2013}+\frac{2}{2012}+\frac{3}{2011}+...+\frac{2011}{3}+\frac{2012}{2}+\frac{2013}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}}\)
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