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SG
0
DP
18 tháng 7 2017
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{2013}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2013}\)
\(\Leftrightarrow x=2013-1=2012\)
TN
14 tháng 6 2017
Có: \(A=\frac{1}{2013}x\frac{2015}{2014}-\frac{2014}{2013}\)
\(=\frac{1}{2013}.\frac{2015}{2014}-\frac{1}{2013}.2014=\frac{1}{2013}.\left(\frac{2015}{2014}-2014\right)\)
LH
3
10 tháng 4 2017
1-\(\frac{1}{2}\)+ \(\frac{1}{3}\) - \(\frac{1}{4}\)+...+\(\frac{1}{2013}\)- \(\frac{1}{2014}\)
=(1+\(\frac{1}{3}\)+...+\(\frac{1}{2013}\)) - (\(\frac{1}{2}\)+ \(\frac{1}{4}\) + ...+ \(\frac{1}{2014}\))
=(1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+...+ \(\frac{1}{2013}\)+ \(\frac{1}{2014}\))-2.(\(\frac{1}{2}\)+ \(\frac{1}{4}\)+...+\(\frac{1}{2014}\))
=1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+ \(\frac{1}{2013}\)+ \(\frac{1}{2014}\)- 1-\(\frac{1}{2}\)-...-\(\frac{1}{1007}\)
=(1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+...+\(\frac{1}{1007}\))+\(\frac{1}{1008}\)+ \(\frac{1}{1009}\)+...+\(\frac{1}{2013}\)+ \(\frac{1}{2014}\)-(1+\(\frac{1}{2}\)+...+\(\frac{1}{1007}\))
=\(\frac{1}{1008}\)+ \(\frac{1}{1009}\)+...+\(\frac{1}{2013}\)+ \(\frac{1}{2014}\).
LH
10 tháng 4 2017
mình chưa hiểu lắm
tại sao nhân 2 lên và còn 1 - \(\frac{1}{2}\)- ... - \(\frac{1}{1007}\)
1007 ở đâu?????
30 tháng 11 2014
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
13 tháng 4 2017
a)\(\frac{2013}{2015}< \frac{2014}{2016}\)
b)\(\frac{2013+2014}{2014+2015}< \frac{2013}{2014}+\frac{2014}{2015}\)
\(\frac{2014.2013-1}{2012.2014+2013}\)
\(=\frac{2012.2014+2014-1}{2012.2014+2013}\)
\(=\frac{2012.2014+2013}{2012.2014+2013}\)
\(=1\)
\(\frac{2014.2013-1}{2012.2014+2013}=1\)