简算题（2道）1/4+1/12+1/24+1/40.1/1802008/2008 2008/2009

4=1*2*2 12=2*3*2 24=3*4*2 40=4*5*2...180=9*10*2
1/4=(1-1/2)*/2,1/12=(1/2-1/3)*/2,1/24=(1/3-1/4)/2...1/180=(1/9-1/10)/2
1/4+1/12+1/24+1/40+...+1/180=[(1-1/2)+(1/2-1/3)+(1/3-1/4)...+(1/9-1/10)]/2=(1-1/10)/2=9/20
下面那道题似乎抄错了吧?!