问题
解答题
求数列
|
答案
设Sn=
+1 2
+3 4
+5 8
+…+7 16 2n-1 2n
则
Sn=1 2
+1 4
+3 8
+…+5 16
+2n-3 2n 2n-1 2n+1
两式相减得
Sn=1 2
+(1 2
+2 4
+2 8
+…+2 16
)-2 2n 2n-1 2n+1
=
+(1 2
+1 2
+1 4
+…+1 8
)-1 2n-1 2n-1 2n+1
=
+1 2
-
[1-(1 2
)n-1]1 2 1- 1 2 2n-1 2n+1
=
-(3 2
)n-1-1 2 2n-1 2n+1
∴Sn=3-
．2n+3 2n