问题
填空题
设f(n)=
|
答案
∵f(n)=
+1 n+1
+2 n+2
+…+1 n+3
(n∈N*),、1 2n
∴f(n+1)=
+1 n+2
+…+1 n+3
+1 2n
+1 2n+1 1 2n+2
∴f(n+1)-f(n)=
+1 n+2
+…+1 n+3
+1 2n
+1 2n+1
-(1 2n+2
+1 n+1
+…+1 n+2
)1 2n
=
+1 2n+1
-1 2n+2 1 n+1
=
-1 2n+1 1 2n+2
故答案为:
-1 2n+1 1 2n+2