考察一般项第n项anan=1/[1+2+...+(n+1)]=1/[(n+1)(n+2)/2]=2/[(n+1)(n+2)]=2[1/(n+1)-1/(n+2)]1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)=2(1/2-1/3+1/3-1/4+...+1/100-1/101+1/101-1/102)=2/(1/2-1/102)=50/51
