un=∫(0→1)[x^n-x^(n+1)]dx=1/(n+1)-1/(n+2)所以，Sn=(1/2-1/3)+(1/3-1/4)+……+[1/(n+1)-1/(n+2)]=1/2-1/(n+2)∵lim Sn=1/2∴级数收敛于1/2
