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1X1/2+1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6+1/6X1/7,...

原式=1/2+1/6+1/12+1/20+1/30+1/42 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7) =1-1/7 =6/7 公式: 1/a乘1/(a+1)=1/a-1/(a+1)其中a是正整数

1x1/2+1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6+1/6x1/7 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/9-1/7 =1-1/7 =6/7

原式=2{(1-1/3)+(1/3-1/5)+(1/5-1/7)……+[1/(2n-1)-1/(2n+1)]} =2[1-1/(2n+1)] 一般看到前后两项是这种类型的都是这种方法的,主要是确定最前面的系数,一般将拆开的两式通一下分就可以求出来了(就是这里最前面的2)

1x1/5+1/5x1/9+1/9x1/13+......+1/2005x1/2009 =(1/4)X(1-1/5+1/5-1/9+1/9-1/13+......+1/2005-1/2009) =(1/4)X(1-1/2009) =(1/4)X(2008/2009) =502/2009

似乎没有简便方法算:1/3+1/5+1/7+...1/101

你化错了. 应该是 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 0

=2x(1-1/3+1/3-1/5+……+1/47-1/49) =2x(1-1/49) =96/49

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