Re: [考古] 政大財政90
※ 引述《lililiu (lily)》之銘言：
: solve the difference equation Y_{t+1} - 3Y_t =1 Y_0 =7/2
: 我爸說這題很難,我也覺得不知道它在幹麻,,,
: 政大好狠 (淚奔)
y(1) - 3y(0) = 1
(1/3)y(2) - y(1) = (1/3)
.........
(1/3)^(n-1) y(n) - (1/3)^(n-2) y(n-1) = (1/3)^(n-1)
3^(1-n) y(n) - 3y(0) = (3/2)[1-(1/3)^n]
=> y(n) = 3^(n-1)[21/2 + 3/2 - (1/2)(1/3)^(n-1)]
= 12 * 3^(n-1) - (1/2)
這不是高中問題?
當場推也不會花多久時間
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