Re: [理工] 台大電機丙遞迴
遞迴這題
我是造一個 {b_n} 數列,其中 b_n = log a_n (以8為底)
這樣就可以轉成:
b_1 = 1, b_2 = 1, b_n = b_{n-1} + 2*b_{n-2}
就變成線性的遞迴惹
接下來解特徵多項式:r^2 - r - 2 = 0
得 r_1 = 2, r_2 = -1
假設 b_n = c*2^n + d*(-1)^n
再代入初值條件解出常數 c = 1/3 和 d = -1/3
而 a_n = 8^{b_n}
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