1/1*2+1/2*3+1/3*4+...+1/100*101+1/101*102
问题描述：
1/1*2+1/2*3+1/3*4+...+1/100*101+1/101*102
答
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(100*101)+1/(101*102)
＝1/2+(1/2 - 1/3)+(1/3 - 1/4)+...+(1/100 -1/100)+(1/101 -1/102) (中间每相邻两项正负相消)
=1/2 +1/2 －1/102
=1－1/102
＝101/102