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C=5/3×7/5×9/7×...2011/2009×2013/2011
C=5×7×9×...×2011×2013/3×5×7×...×2009×2011
C=2013/3
C=674
Nếu sai bảo mình nhé !
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C=5/3.7/5.9/7....................2011/2009.2013/2011
=5.7.9...........2011.2013/3.5.7.............2009.2011
=2013/3
=671
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\left(1+\frac{2}{3}\right)\cdot\left(1+\frac{2}{5}\right)\cdot\left(1+\frac{2}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1+\frac{2}{2009}\right)\cdot\left(1+\frac{2}{2011}\right)\)
\(C=\frac{5}{3}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\cdot\cdot\cdot\cdot\frac{2011}{2009}\cdot\frac{2013}{2011}\)
\(C=\frac{5\cdot7\cdot9\cdot\cdot\cdot\cdot\cdot2011\cdot2013}{3\cdot5\cdot7\cdot\cdot\cdot\cdot\cdot2009\cdot2011}\)
\(C=\frac{2013}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) -1 - 2 - 3 - 4 - 5 -.............- 2009 - 2010
SCSH: ( 2010 - 1 ) : 1 + 1 = 2010
tỔNG: ( 2010 + 1 ) . 2010 : 2 = 2021055
b) 1 - 3 + 5 - 7 +...............+ 2005 - 2007 + 2009 - 2011
SCSH: ( 2011 - 1 ) : 2 + 1 = 1006
tỔNG: ( 2011 + 1 ) . 1006 : 2 = 1012036
c) 1 - 2 - 3 + 4 + 5 - 6 - 7 +..........................+ 1997 - 1998 - 1999 + 2000 + 2001
SCSH: ( 2001 - 1 ) : 1 + 1 = 2001
tỔNG: ( 2001 + 1 ) . 2001 : 2 = 2003001
Hk tốt,
k nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(C=\left(1+\frac{2}{3}\right)\left(1+\frac{2}{5}\right)\left(1+\frac{2}{7}\right).....\left(1+\frac{2}{2009}\right)\left(1+\frac{2}{2011}\right)\) ta có :
\(C=\left(\frac{3+2}{3}\right)\left(\frac{5+2}{3+2}\right)\left(\frac{7+2}{5+2}\right).....\left(\frac{2009+2}{2007+2}\right)\left(\frac{2011+2}{2009+2}\right)\)
\(C=\frac{\left(3+2\right)\left(5+2\right)\left(7+2\right).....\left(2009+2\right)\left(2011+2\right)}{3\left(3+2\right)\left(5+2\right).....\left(2007+2\right)\left(2009+2\right)}\)
\(C=\frac{2011+2}{3}\)
\(C=\frac{2013}{3}\)
\(C=671\)
Vậy \(C=671\)
Chúc bạn học tốt ~
![](https://rs.olm.vn/images/avt/0.png?1311)
C=(1+2/3).(1+2/5).(1+2/7)......(1+2/2009).(1+2/2011)
C=5/3.7/5.9/7......2011/2009.2013/2011
C=5.7.9.....2013/3.5.7.....2009.2011
C=2013/3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3x\left(2x+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x+1=0\\3x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=-1\\x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=0\end{cases}}\)
\(\frac{\frac{6}{5}+\frac{6}{35}-\frac{6}{125}-\frac{6}{2009}-\frac{6}{2011}}{\frac{7}{5}+\frac{7}{35}-\frac{7}{125}-\frac{7}{2009}-\frac{7}{2011}}\)
\(=\frac{6.(\frac{1}{5}+\frac{1}{35}-\frac{1}{125}-\frac{1}{2009}-\frac{1}{2011})}{7.(\frac{1}{5}+\frac{1}{35}-\frac{1}{125}-\frac{1}{2009}-\frac{1}{2011})}\)
\(=\frac{6}{7}\)
Tìm x
\(a,3x(2x+1)=0\)
\(\Rightarrow\hept{\begin{cases}3x=0\\2x+1=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=0\\x=\frac{-1}{2}\end{cases}}\)
Vậy \(x=0\)hoặc \(x=\frac{-1}{2}\)
\(b.\frac{2}{3}-\frac{1}{3}(x-\frac{3}{2})-\frac{1}{2}(2x+1)=5\)
\(\frac{2}{3}-\frac{1}{3}x+\frac{1}{2}-x-\frac{1}{2}=5\)
\(\frac{2}{3}+\frac{1}{2}-\frac{1}{2}-x(\frac{1}{3}+1)=5\)
\(\frac{4}{3}x=\frac{2}{3}-5\)
\(\frac{4}{3}x=\frac{-13}{3}\)
\(x=\frac{-13}{3}\div\frac{4}{3}\)
\(x=\frac{-13}{4}\)
Chúc ban học tốt
\(C = \frac{5}{3} . \frac{7}{5} . ... \frac{2013}{2011}\)
\(C = \frac{5.7.9....2011.2013}{3.5.7...2011}\)
\(C = \frac{5.2013}{3} = \frac{10065}{3} = 3355\)