1:
1/(3*5)+1/(5*7)+1/(7*9)+...+1/(2007*2009)
==1/2*(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)...+1/2(1/2007-1/2009)
=1/2*(1/3-1/5+1/5-1/7+1/7-1/9...+1/2007-1/2009)
=1/2(1/3-1/2009)=1003/6027;
2:
因为
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10=1;
所以:
(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+1/10=1;
所以:
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10=1;
所以倒数和为1的十个数分别为2,6,12,20,30,42,56,72,90,10;