1/1*2+1/2*3+1/3*4+...+1/2008*2009
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1/1*2+1/2*3+1/3*4+...+1/2008*2009
我看过别人的解答:1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008
=[1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008]
=1-1/2008
=2007/2008
但是还是不懂:为什么从原式1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008就 变成=[1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008]了呢?跟减法有什么关系呢?
我看过别人的解答:1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008
=[1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008]
=1-1/2008
=2007/2008
但是还是不懂:为什么从原式1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008就 变成=[1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008]了呢?跟减法有什么关系呢?
1/1*2
=(2-1)/1*2
=2/1*2-1/1*2
=1-1/2
1/2*3
=(3-2)/(2*3)
=3/(2*3)-2/(2*3)
=1/2-1/3
1/3*4
=(4-3)/3*4
=4/3*4-3/3*4
=1/3-1/4
后面以此类推
就得到1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
=(2-1)/1*2
=2/1*2-1/1*2
=1-1/2
1/2*3
=(3-2)/(2*3)
=3/(2*3)-2/(2*3)
=1/2-1/3
1/3*4
=(4-3)/3*4
=4/3*4-3/3*4
=1/3-1/4
后面以此类推
就得到1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
计算:|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2009-1/2008|
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+.+(-1/2008*1/2009)+(-1/2009*1
|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
计算:|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2008-1/2007|+|1/2009-1
1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
计算1×1!+2×2!+3×3!+4×4!+…2008×2008!+2009×2009!
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2008×1/2009)
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)×(1-1/3)×(1-1/4)×.×(1-1/2008)×(1-1/2009)这道题怎么简算?
(1/2010-1)*(1/2009-1)*(1/2008-1)*...*(1/3-1)*(1/2-1)
1/2009-1/2008|+|1/2008-1/2007|+|1/2007-1/2006|+.+|1/3-1/2|+|