an=[(n+2)-(n-1)]/(n+1)(n+2)=(n+1)/(n+1)(n+2)-(n+1)/(n+1)(n+2)=1/(n+1)-1/(n+2)所以S100=1/2-1/3+1/3-1/4+……+1/101-1/102=1/2-1/102=25/51
