1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
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1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
![1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=](/uploads/image/z/17253135-63-5.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B...%2B1%2F2008%2A1%2F2009%2A1%2F2010%3D)
首先,1/(n(n+1)(n+2))=1/2[1/(n(n+1))-1/((n+1)(n+2))]
所以,1/1*2*3=1/2[1/1*2-1/2*3]
1/2*3*4=1/2[1/2*3-1/3*4]
.
1/2008*1/2009*1/2010=1/2[1/2008*2009-1/2009*2010]
1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=1/2[1/1*2-1/2009*2010]=504761/2019045
所以,1/1*2*3=1/2[1/1*2-1/2*3]
1/2*3*4=1/2[1/2*3-1/3*4]
.
1/2008*1/2009*1/2010=1/2[1/2008*2009-1/2009*2010]
1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=1/2[1/1*2-1/2009*2010]=504761/2019045
|1/2-1|+|1/3-1/2|+1/4-1/3|+...|1/2009-1/2008|+|1/2010-1/2009
"1*2/1+2*3/1+3*4/1+.+2007*2008/1+2008*2009/1+2009*2010/1"这道题
(1/2010*1/2009*1/2008*...*1/3*1/2*1)^2011*(2010*2009*2008*..
1+2+3+4……+2008+2009+2010=?
(1/2010-1)*(1/2009-1)*(1/2008-1)*...*(1/3-1)*(1/2-1)
|1/2011-1/2010|+|1/2011-1/2009|+|1/2009-1/2008|+...+|1/3-1/2
1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
计算:|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2009-1/2008|
计算1/1*2010+1/2*2009+1/3*2008+...+1/2010*1-2010/2011(1/1*2009
初一数学题计算(-1*1/2)+(-1/2*1/3)=(-1/3*1/4)+...+(1/2008*1/2009)
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+.+(-1/2008*1/2009)+(-1/2009*1
1×2分之1+2×3分之1+3×4分之1+……+2008×2009分之1+2009×2010分之1=?