问题
填空题
设S1=1+
设S=
|
答案
∵Sn=1+
+1 n2
=1 (n+1)2
=n2(n+1)2+(n+1)2+n2 n2(n+1)2
=[n(n+1)]2+2n2+2n+1 [n(n+1)]2
，[n(n+1)+1]2 [n(n+1)]2
∴
=Sn
=1+n(n+1)+1 n(n+1)
-1 n
，1 n+1
∴S=1+1-
+1+1 2
-1 2
+…+1+1 3
-1 n 1 n+1
=n+1-1 n+1
=
=(n+1)2-1 n+1
．n2+2n n+1
故答案为：
．n2+2n n+1