注意到1/n*(n+1)*(n+2)=1/2*[1/n*(n+1)-1/(n+1)(n+2)]=
1/2{[1/n-1/(n+1)]-[1/(n+1)-1/(n+2)]}=1/2*[1/n-2/(n+1)+1/(n+2)]
所以原式=1/2[(1-1/101)-(1/2-1/102)]=50/101-25/102
注意到1/n*(n+1)*(n+2)=1/2*[1/n*(n+1)-1/(n+1)(n+2)]=
1/2{[1/n-1/(n+1)]-[1/(n+1)-1/(n+2)]}=1/2*[1/n-2/(n+1)+1/(n+2)]
所以原式=1/2[(1-1/101)-(1/2-1/102)]=50/101-25/102