1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9).+1/2011×2013= 怎么算 求方法

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1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9).+1/2011×2013= 怎么算 求方法
1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9).+1/2011×2013= 怎么算 求方法

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9).+1/2011×2013= 怎么算 求方法
列项,1/n(n 2)=(1/2)(「1/n 」-「 1/(n 2)」) 每项都如此拆,最后就只剩(1/2)(1-(1/2013))
一般这种分母如此变化的题都是列项^^

1、1、2、3、5、( )、( ). 简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7) 算术题,(1+1/3+1/5+1/7)×(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)×(1/3+1/5+1/7) 1.(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)=2.(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)= 1/1*3=1/2(1-1/3)1/3*5=1/2(1/3-1/5)1/5*7=1/2(1/5-1/7).1/17*19=1/2(1/17-1/19)所以1/1*3+1/3*5+1/5*7+.1/17*19=1/2(1-1/3)+1/2(1/3+1/5)+1/2(1/5-1/7)+.1/2(1/17-1/19)=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7.+1/17-1/19)=1/2(1-1/1 数奥题(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7)求(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7)的简便算法要求: (1+2/1)(1+4/1)(1+6/1).(1+10/)(1-3/1)(1—5/1).(1-9/1) 1,1,1,3,5,9,( ),( ) 计算 ( 1+1/2)*(1-1/3)*(1+1/4)*(1-1/5)*.*(1+1/1000)*(1-1/1001) 1,1,2,3,3,5,( ),( ) (2*3*4*5)*(1/2-1/3-1/4-1/5) 3/5-3/1表示( ) 数学题(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670)=? 1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6 (简便方法) 1,2,3,5,( ),( ),21. +2006)-(1+3+5+.+2005) (1-1/2)*(1/3-1)*(1-1/4)*(1/5-1)…(1/2009-1)*(1-1/2010)等于多少 (1-2/1)3/1-1)(1-4/1)(5/1-1)…(2009/1-1)(1-2010/1)等于几?