（1）︱1/3+（-1/2）︱+︱1/4+（-1/3）︱+︱1/5+（-1/4）︱+.+︱1/2010+（-1/2009）︱
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/2009-1/2010)
=1/2-1/2010
=502/1005
(2)1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-1/4;.
1/1*2=(2-1)/2*1=2/(2*1)-1/(2*1)=1-1/2
1/2*3=(3-2)/(2*3)=3/(2*3)-2/(2*3)=1/2-1/3
1/3*4=(4-3)/(4*3)=4/(4*3)-3/(4*3)=1/3-1/4
推理：
1/（n-1)*n=1/(n-1)-1/n