Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
#)Giải :
\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\left(\frac{1}{6}+\frac{1}{3}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\left(\frac{1}{2}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\times0\)
\(=0\)
\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).\left(\frac{1}{6}+\frac{1}{3}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).\left(\frac{1}{6}+\frac{2}{6}+\frac{3}{6}\right)\)
=\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).0\)
\(=0\)
Mẫu số = 2014.2012.100010001 - 2012.2014.100010001 = 0
Vậy phân số trên vô nghĩa vì mẫu số bằng 0.
\(A=\frac{1}{2\times4}+\frac{1}{4\times6}+\frac{1}{6\times8}+...+\frac{1}{2012\times2014}\)
\(=\frac{1}{2}\times(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2012\times2014})\)
\(=\frac{1}{2}\times(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2012}-\frac{1}{2014})\)
\(=\frac{1}{2}\times(\frac{1}{2}-\frac{1}{2014})\)
\(=\frac{1}{2}\times(\frac{1007}{2014}-\frac{1}{2014})\)
\(=\frac{1}{2}\times\frac{503}{1007}\)
\(=\frac{503}{2014}\)
Ta có ; \(\frac{1}{2}=\frac{1007}{2014}\)
Vậy A bé hơn B
Chúc bạn học tốt
Ta có : 1 - 2012/2015 = 3/2015
1 - 2015/2018 = 3/2018
Vì 3/2015 > 3/2018 nên 2012/2015 < 2015/2018
1-2012/2015=3/2015
1-2015/2018=3/2018
Vì 3/2015>3/2018=>2012/2015<2015/2018
mỗi số hạng trong biểu thức A đều nhỏ hơn 1 mà có 15 số nên tổng A sẽ nhỏ hơn 15
ta thay tong tren <1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
hay tong tren be hon 15
\(\frac{2011.2013+2014}{2012.2012+2013}=\frac{2011.2013+2013+1}{2012.2012+2012+1}=\frac{2013.\left(2011+1\right)+1}{2012.\left(2012+1\right)+1}=\frac{2013.2012+1}{2012.2013+1}=1\)
Vậy \(\frac{2011.2013+2014}{2012.2012+2013}=1\)
(Dấu . là nhân nha bạn)
Ta có \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2012+2013}\)
\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011+2012}{2012+2013}\)(ĐPCM)
Học tốt