问题
填空题
数列S
|
答案
Sn=
+1 2
+3 22
…+5 23 2n-1 2n
Sn=1 2
+1 22
+3 23
+…+5 24
+2n-2 2n 2n-1 2n+1
两式相减得
Sn=1 2
+1 2
+2 22
+…+2 23
-2 2n
=2n-1 2n+1
+1 2
-
(1-1 4
)1 2n-1 1- 1 2
=2n-1 2n+1
-3 2 2n-1 2n+1
∴Sn=3-2n+3 2n
故答案为:3-2n+3 2n