解:Sn=1+1/n²+1/(n+1)²
={n²(老乎拍n+1)²+n²+(n+1)²}/{n²(n+1)²}
={n²(n+1)²+2n(n+1)+1}/{n²顷弊(n+1)²}
={n(n+1)+1}²/{n²(n+1)²}
所以S=根号S1+根号S2+……+根号Sn
=3/2+7/6+........+{n(n+1)+1}/{n(n+1)}
={1+1/(1*2)}+{1+1/(2*3)}+.......{1+1/(n(n+1))}
=n+1/(1*2)+1/(2*3)+.....1/{n(n+1)}
=n+(1-1/2)+(1/2-1/3)+.....+(1/n-1/(n+1))
=n+1-1/2+1/2+1/3-1/4+1/侍羡4+....+1/n-1/(n+1)
=n+1-1/(n+1)
=n(n+2)/(n+1)
S=(6+根号21)|4+根号(n4次方+2n3次方+2n平方+2n+1)|n(n+1)
好难呀