2/1 x 3 + 2/3 x 5 +........+ 2/(X - 2) x X = 1994/1995
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NB
1
30 tháng 3 2019
Suy ra \(\frac{x+1}{1999}+1+\frac{x+2}{1998}+1=\frac{x+3}{1997}+1+\frac{x+4}{1996}\)
Suy ra \(\frac{x+2000}{1999}+\frac{x+2000}{1998}=\frac{x+2000}{1997}+\frac{x+2000}{1996}\)
Suy ra \(\frac{x+2000}{1999}+\frac{x+2000}{1998}-\frac{x+2000}{1997}-\frac{x+2000}{1996}=0\)
Suy ra \(x+2000.\left(\frac{1}{1999}+\frac{1}{1998}-\frac{1}{1997}-\frac{1}{1996}\right)=0\)
Vì \(\left(\frac{1}{1999}+\frac{1}{1998}-\frac{1}{1997}-\frac{1}{1996}\right)\ne0\)
Suy ra x+2000=0
Suy ra x=-2000
Hok tốt
LH
1
3 tháng 5 2015
a. 3/5 + 6/11 + 7/13 + 2/5 + 16/11 + 19/13
= ( 3/5 + 2/5 ) + ( 6/11 + 16/11 ) + ( 7/13 + 19/13)
= 1 + 2 + 2
= 5.
MN
10 tháng 4 2016
a) \(\frac{3}{5}+\frac{6}{11}+\frac{7}{13}+\frac{2}{5}+\frac{16}{11}+\frac{19}{13}\)
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)\)
\(=1+2+2=5\)
b) \(\frac{1995}{1997}x\frac{1990}{1993}x\frac{1997}{1994}x\frac{1993}{1995}x\frac{997}{995}=\frac{1995x1990x1997x1993x997}{1997x1993x1994x1995x995}=\frac{1990x997}{1994x995}=\frac{995x2x997}{997x2x995}=1\)
TN
10 tháng 4 2016
a) =(3/5+2/5)+(6/11+16/11)+(19/13+7/13)
=5/5+22/11+26/13
=1+2+3
=6
NT
1
9 tháng 8 2018
\(\dfrac{x-1}{1992}+\dfrac{x-2}{1993}=\dfrac{x-3}{1994}+\dfrac{x-4}{1995}\)
\(\Rightarrow\left(\dfrac{x-1}{1992}+1\right)+\left(\dfrac{x-2}{1993}+1\right)=\left(\dfrac{x-3}{1994}+1\right)+\left(\dfrac{x-4}{1995}+1\right)\)
\(\Rightarrow\left(\dfrac{x-1+1992}{1992}\right)+\left(\dfrac{x-2+1993}{1993}\right)=\left(\dfrac{x-3+1994}{1994}\right)+\left(\dfrac{x-4+1995}{1995}\right)\)
\(\Rightarrow\dfrac{x+1991}{1992}+\dfrac{x+1991}{1993}=\dfrac{x+1991}{1994}+\dfrac{x+1991}{1995}\)
\(\Rightarrow\dfrac{x+1991}{1992}+\dfrac{x+1991}{1993}-\dfrac{x+1991}{1994}-\dfrac{x+1991}{1995}=0\)
\(\Rightarrow\left(x+1991\right)\left(\dfrac{1}{1992}+\dfrac{1}{1993}-\dfrac{1}{1994}-\dfrac{1}{1995}\right)=0\)
\(\Rightarrow\left(x+1991\right)=0\) ( vì \(\left(\dfrac{1}{1992}+\dfrac{1}{1993}-\dfrac{1}{1994}-\dfrac{1}{1995}\right)\ne0\)
\(\Rightarrow x=-1991\)
\(1-\dfrac{1}{x}=\dfrac{1994}{1995}\)
\(\dfrac{1}{x}=\dfrac{1}{1995}\)
x= 1995
\(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) +...+ \(\dfrac{2}{\left(x-2\right)\times x}\) = \(\dfrac{1994}{1995}\)
\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) +...+ \(\dfrac{1}{x-2}-\dfrac{1}{x}\) = \(\dfrac{1994}{1995}\)
1 - \(\dfrac{1}{x}\) = \(\dfrac{1994}{1995}\)
\(\dfrac{1}{x}\) = 1 - \(\dfrac{1994}{1995}\)
\(\dfrac{1}{x}\) = \(\dfrac{1}{1995}\)
\(x\) = 1995