问题
解答题
计算: (1-
(1-
(1-
(1-
|
答案
(1-
)×(1-1 22
)=1 32
×3 4
=8 9
;2 3
(1-
)×(1-1 22
)×(1-1 32
)=1 42
×2 3
=15 16
=5 8
;4+1 2×4
(1-
)×(1-1 22
)×(1-1 32
)×(1-1 42
)=1 52
×5 8
=24 25
=3 5
;5+1 2×5
依此类推:(1-
)×(1-1 22
)×…×(1-1 32
)×(1-1 92
)=1 102
=10+1 2×10
;11 20
(1-
)×(1-1 22
)×…×(1-1 32
)×(1-1 (n-1)2
)=1 n2
.n+1 2n
故答案为:
;2 3
;5 8
;11 20 n+1 2n