问题
解答题
已知数列an=(n+1)×(
|
答案
∵an=n+1为等差数列，bn=(
)n为等比数列9 10
∵Sn=2×
+3×(9 10
)2+…+(n+1)•(9 10
)n9 10
∴
Sn=2×(9 10
)2+3×(9 10
)3+…+(n+1)×(9 10
)n9 10
两式相减，
Sn=1 10
+[(9 5
)2+(9 10
)3+…+(9 10
)n]-(n+1)•(9 10
)n+19 10
=
+9 5
×[1- (81 10
)n ]-(n+1)×(9 10
)n+19 10
=
-(99 10
)n+1(n+10)9 10
∴Sn=99-9(n+10)×(
)n9 10