六年级数学题/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+.+1/(99*100)=?1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+......+1/(99*100)=?
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六年级数学题/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+.+1/(99*100)=?1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+......+1/(99*100)=?
六年级数学题/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+.+1/(99*100)=?
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+......+1/(99*100)=?
六年级数学题/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+.+1/(99*100)=?1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+......+1/(99*100)=?
原式=1-1/2+1/2-1/3+1/3-1/4.+1/99-1/100=1-1/100=99/100
因为1/(1*2)=1-1/2；1/(2*3)=1/2-1/3；1/(3*4)=1/3-1/4......以此类推
所以，原式=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）......+(1/99-1/100)=1-1/100=99/100
从这道题中，你会发现一个规律，那就是：1/（a*（a+1））=1/a-1/（a+1）（其中，a>0)
=1-1/2+1/2-1/3+1/3-1/4。。。。。。。。1/98-1/99+1/99-1/100=99/100
答案：99/100
解题方法：=（1/1-1/2）+（1/2-1/3）+(1/3-1/4)+......+(1/99-1/100)
=1-1/100
=99/100