micke1
幼苗
共回答了22个问题采纳率:86.4% 举报
A=1/1*2+1/3*4+1/5*6+.+1/1999*2000
=1-1/2+1/3-1/4+1/5-1/6+……1/1999-1/2000
=(1+1/3+1/5+1/7+…..+1/1999)-( 1/2+1/4+1/6+…..1/2000)
=(1+1/2+1/3+1/4+……+1/2000)-( 1/2+1/4+1/6+…..1/2000)*2
=(1+1/2+1/3+1/4+……+1/2000)- (1+1/2+1/3+……+1/1000)*1/2*2 后面括号提取1/2
=(1+1/2+1/3+1/4+……+1/2000)- (1+1/2+1/3+……+1/1000)
=1/1001+1/1002+.+1/1999+1/2000
.B=1/1000+1/1001+1/1002+.+1/1999
= 1/1001+1/1002+.+1/1999+1/1000
A和 B前999位都是1/1001+1/1002+.+1/1999,最后一位不同,所以因为1/2000
1年前
4