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LN
1
13 tháng 8 2016
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
=> \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
=> \(2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2011}{2013}\)
=> \(2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
=> \(2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
=> \(2.\frac{1}{2}-2.\frac{1}{x+1}=\frac{2011}{2013}\)
=> \(1-\frac{2}{x+1}=\frac{2011}{2013}\)
=> \(\frac{2}{x+1}=1-\frac{2011}{2013}=\frac{2}{2013}\)
=> x + 1 = 2013
=> x = 2013 - 1 = 2012
XO
5 tháng 1 2020
Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
=> \(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2011}{2013}\)
=> \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2011}{4026}\)
=> \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2011}{4026}\)
=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4016}\Rightarrow\frac{1}{x+1}=\frac{1}{2013}\Rightarrow x+1=2013\Rightarrow x=2012\)
H
0
TT
1
NM
0
TN
1
4 tháng 7 2016
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2009}{2011}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2009}{2011}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2011}\)
\(x+1=2011\)
\(x=2010\)
HT
0
1/2x3/2+1/3x4/2+1/4x5/2+1/5x6/2+.......+2/Xx(X+1)=2011/2013
2/2x3+2/3x4+2/4x5+2/5x6+.....+2/Xx(X+1)=2011/2013
2x(1/2x3+1/3x4+1/4x5+1/5x6+....+1/Xx(x+1)=2011/2013
1/2x3+1/3x4+1/4x5+1/5x6+....+1/Xx(X+1)=2011/4026
1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.....+ 1/x-1/x+1=2011/4026
1/2-1/x+1=2011/4026
1/x+1=1/2-2011/4026
1/x+1=1/2013
Suy ra x=2012
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