速算：(1×3)分之1＋(3×5)分之1＋(5×7)分之1…＋(2001×2003)分之1

(1×3)分之1＋(3×5)分之1＋(5×7)分之1…＋(2001×2003)分之1

=1/2(1-1/2+1/3-1/5+…………+1/2001-1/2003)

=1/2(1-1/2003)

=1001/2003

此方法叫做拆项相消

=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)...+1/2(1/2001-1/2003)
=1/2(1-1/3+1/3-1/5+1/5-1/7...+1/2001-1/2003)
=1/2(1-1/2003)
=1001/2003

好做呀
原式=1/2*[（1/1-1/3）+(1/3-1/5)+...+(1/2001-1/2003)]=1/2*(1-1/2003)=1001/2003

等于1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+ +1/2*(1/2001-1/2003)=1/2*(1-1/2003)
=1001/2003

原式=（1-1/3+1/3-1/5+1/5-1/7+…+1/2001-1/2003）/2
=（1-1/2003）/2
=1001/2003

原式=1/2×（1-1/3）+1/2×（1/3-1/5）+1/2×（1/5-1/7）+……1/2×（1/2001-1/2003）

=1/2×（1-1/2003）

=1001/2003