A.9
B.10
C.11
D.12
E.56
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1題CE 數.
2011-07-25 2:21 am
1. If the product of the first n terms of the sequence 10,10^2,10^3,...,10^n exceeds 10^55, find the minimum value of n.
A.9
B.10
C.11
D.12
E.56
A.9
B.10
C.11
D.12
E.56
回答 (1)
2011-07-25 2:44 am
✔ 最佳答案
10 x 10² x 10³ x ... x 10ⁿ > 10⁵⁵
10⁽¹ ⁺ ² ⁺ ³ ⁺ "" ⁺ ⁿ⁾ > 10⁵⁵
1 + 2 + 3 + ... + n > 55
n(n+1)/2 > 55
n² + n - 110 > 0
(n - 10)(n + 11) > 0
n < - 11 (rejected) or n > 10
n(min.) = 11
(C)
收錄日期: 2021-04-21 22:22:02
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