＝1/2－1/3＋1/3－1/4＋1/4－1/5＋......＋1/2008－1/2009
＝1/2－1/2009
＝2009/4018－2/4018
＝2007/4018
1\/2X3+1\/3X4+1\/4X5+~~~1\/2008X2009找规律,算结果
一休08252，你好：1\/2×3＋1\/3×4＋1\/4×5＋...＋1\/2008×2009 ＝1\/2－1\/3＋1\/3－1\/4＋1\/4－1\/5＋...＋1\/2008－1\/2009 ＝1\/2－1\/2009 ＝2009\/4018－2\/4018 ＝2007\/4018
数学题。急求高手解答1\/1x2+1\/2x3+1\/3x4+1\/4x5+...+1\/2007x2008+1\/200...
1\/1x2+1\/2x3+1\/3x4+1\/4x5+...+1\/2007x2008+1\/2008x2009 =（1-1\/2）+（1\/2-1\/3）+（1\/3-1\/4）+...+（1\/2008-1\/2009）=1-1\/2009 =2008\/2009 学了数列 裂项 后 就会做了
1\/2x3十1\/3x4+1\/4x5+…+1\/99x100简便计算
1\/(2*3) + 1\/(3*4) + 1\/(4*5) + ...+ 1\/(99*100)= (1\/2 - 1\/3) + (1\/3 - 1\/4) + (1\/4 - 1\/5) + ...+ (1\/99 - 1\/100)= 1\/2 +(1\/3 - 1\/3) + (1\/4 - 1\/4) + ...+ (1\/99 - 1\/99) - 1\/100= 1\/2 - 1\/100= 0.49 ...
1x2x3+2x3x4+...+48x49x50帮个忙解下
1*2*3=(1*2*3*4-0*1*2*3)\/(4-0)，括号里1*2*3是公因数，提出后剩下(4-0),把它除掉就是1*2*3了 2*3*4=(2*3*4*5-1*2*3*4)\/(5-1)， 同理 ...n*(n+1)(n+2)=[n*(n+1)(n+2)(n+3)-(n-1)n*(n+1)(n+2)]\/[(n+3)-(n-1)]分母都是4 相加，...
1\/2+1\/2x3+1\/3x4+1\/4x5...1\/2009x2010
原式=1\/(1*2)+1\/(2*3)+1\/(3*4)+...+1\/(2009*2010)=(1-1\/2)+(1\/2-1\/3)+(1\/3-1\/4)+...+(1\/2009-1\/2010)=1+(-1\/2+1\/2)+(-1\/3+1\/3)+...+(-1\/2009+1\/2009)-1\/2010 =1+0+0+0+...+0-1\/2010=1-1\/2010=2009\/2010 ...
...1\/1x2+1\/2x3+1\/3x4+1\/4x5+...1\/2005x2006怎么算?说明思路.谢谢!_百...
解:根据两个连续自然数A,B.1\/A-1\/B=1\/AB得 原式 =1-1\/2+(1\/2-1\/3)+(1\/4-1\/3)+(1\/5-1\/4)+...+(1\/2006-1\/2005)=1-1\/2+1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+1\/5+...+1\/2005-1\/2006)=1-1\/2006 =2005\/2006....
...1\/1x2+1\/2x3+1\/3x4+1\/4x5+...+1\/2007x2008=多少 怎么计算
1\/1x2+1\/2x3+1\/3x4+1\/4x5+...+1\/2007x2008(任何一项积分母分之一可化成两个互减单项式形式,没什么公式,只是个特例)=(1\/1-1\/2)+ (1\/2-1\/3)+(1\/3-1\/4)+(1\/4-1\/5)+,,,+(1\/2007-1\/2008)=1-1\/2+1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+...+1\/2007-1\/2008 =1-1\/...
2x3分之1+3x4分之1+4x5分之1...+99x100分之1,用简便方法计算
裂项
1\/1x2x3+1\/2x3x4+1\/3x4x5
解1\/(1+2+3)+1\/(2+3+4)+1\/(3+4+5)……+1\/(99+100+101)=1\/6+1\/9+1\/12+1\/15...+1\/300 =1\/3*(1\/2+1\/3...+1\/99+1\/100)=1\/3*4.18737751763961 =1.39579250587987
简便计算1\/2+1\/2x3+1\/3x4+1\/4x5+...+1\/99x100
1\/2+1\/2x3+1\/3x4+1\/4x5+...+1\/99x100 = 1\/2 + (1\/2 - 1\/3)+(1\/3 - 1\/4) +... +(1\/99 - 1\/100)= 1\/2 +1\/2 -1\/3+1\/3 -1\/4+1\/4+...+1\/99 - 1\/100 = 1 - 1\/100 =99\/100 (*^__^* *^__^* *^__^*)有什么不明白可以对该题继续追问，随...
