解:原式=1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)+1/(11*12)=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12=1/6-1/12=1/12
=(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)+(1/11-1/12)=1/6-1/12=1/12
