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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
Ta có: 3<4<5<6<7<8<9<2000<2009<2010<2013<2015
=>\(\frac13>\frac14>\frac15>\frac16>\frac17>\frac18>\frac19>\frac{1}{2000}>\frac{1}{2009}>\frac{1}{2010}>\frac{1}{2013}>\frac{1}{2015}\)
=>\(\frac13+1>\frac14+1>\frac15+1>\frac16+1>\frac17+1>\frac18+1>\frac19+1>\frac{1}{2000}+1>\frac{1}{2009}+1>\frac{1}{2010}+1>\frac{1}{2013}+1>\frac{1}{2015}+1\)
=>\(\frac43>\frac54>\frac65>\frac76>\frac87>\frac98>\frac{10}{9}>\frac{2001}{2000}>\frac{2010}{2009}>\frac{2011}{2010}>\frac{2014}{2013}>\frac{2016}{2015}\)
#)Giải :
\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\left(\frac{1}{6}+\frac{1}{3}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\left(\frac{1}{2}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2016}+\frac{2009}{2018}\right)\times0\)
\(=0\)
\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).\left(\frac{1}{6}+\frac{1}{3}+\frac{1}{2}\right)\)
\(=\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).\left(\frac{1}{6}+\frac{2}{6}+\frac{3}{6}\right)\)
=\(\left(\frac{2012}{2015}+\frac{2011}{2016}+\frac{2010}{2017}+\frac{2009}{2018}\right).0\)
\(=0\)
a) \(\frac{47}{32}>\frac{36}{46}\)Vì phân số \(\frac{47}{32}>1;\frac{36}{46}< 1\)nên \(\frac{47}{32}>\frac{36}{46}\)
b) \(\frac{199}{200}< \frac{200}{201}\)Vì \(\frac{199}{200}=\frac{199.201}{200.201};\frac{200}{201}=\frac{200.200}{201.200}\)
ta so sánh 199.201 và 200.200
199.201 = 199.(200+1) = 199.200+199
200.200 = 200.(199+1) = 200.199+200
Vì 199.200 + 199 < 200.199+200 nên \(\frac{199}{200}< \frac{200}{201}\)
c) \(\frac{2012.2010}{2011.2011}=\frac{\left(2011+1\right).2010}{2011.\left(2010+1\right)}=\frac{2011.2010+2010}{2011.2010+2011}\)
\(\frac{2013.2009}{2014.2008}=\frac{2013.\left(2008+1\right)}{\left(2013+1\right).2008}=\frac{2013.2008+2013}{2013.2008+2008}\)
ta so sánh : \(\frac{2010}{2011}< \frac{2013}{2008}\) vì \(\frac{2010}{2011}< 1;\frac{2013}{2008}>1\)
\(\frac{2}{5}\cdot\frac{1}{2}-\frac{2}{5}\cdot\frac{1}{3}-\frac{2}{5}\cdot\frac{1}{6}\)
\(=\frac{2}{5}\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\frac{2}{5}\cdot\frac{0}{6}=\frac{2}{5}\cdot0=0\)
tìm x
a) \(0,5+\left(x-\frac{15}{2}\right):\frac{1}{2}=\frac{9}{2}\)
\(\Rightarrow x=\frac{19}{2}=8,5\)
b) \(2012\cdot x-2010\cdot x=2014\)
\(\Leftrightarrow\left(2012-1010\right)\cdot x=2014\)
\(\Leftrightarrow2x=2014\)
\(\Rightarrow x=\frac{2014}{2}=1007\)
hok tốt .
Tính nhanh:
2/5 x 1/2 - 2/5 x 1/3 - 2/5 x 1/6
= 2/5 x ( 1/2 - 1/3 - 1/6 )
= 2/5 x ( 3/6 - 2/6 - 1/6 )
= 2/5 x 0/6
=0
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$