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等比級數數學解題
Oct 2nd 2013, 14:57

版大你好~
此題為等比級數的問題～

首項為 a = 1
公比為 r = 2
數列為 1, 2, 4, 8, ...
這裏
T(1) = 1
T(2) = 2
T(3) = 4
...
T(n) = a*r^(n-1) = 1*2^(n-1) = 2^(n-1)

題目希望求 n 使
T(1) + T(2) + ... + T(n) ≥ 3650000
即 S(n) ≥ 3650000
a*(1-r^n)/(1-r) ≥ 3650000
1*(1-2^n)/(1-2) ≥ 3650000
2^n-1 ≥ 3650000
2^n ≥ 3650001
log 2^n ≥ log 3650001
n*log 2 ≥ log 3650001
n ≥ (log 3650001)/(log 2)
n ≥ 21.79946543
n ≥ 22

意指要到 n = 22 日才能搬完全部的3650000個柚子。

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