因为对于正整数n,1/[n*(n+1)*(n+2)]=[1/(2n)]-[1/(n+1)]+{1/[2*(n+2)]}原式=(1/4）-(1/3)+(1/8)+(1/6)-(1/4)+(1/10)+(1/8)-(1/5)+(1/12)+(1/10)-(1/6)+(1/14)+(1/12)-(1/7)+(1/16)+(1/14)-(1/8)+(1/18)+(1/16)-(1/9)...