Herman Yeung Blog: 疑似 HKMO 題目 2

2016年5月24日星期二

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匿名說...: Just to offer an alternative approach.

From equation (1),
x_2 = 1 - x_1
Also,
x_n + x_(n+1) = x_(n+1) + x_(n+2) for n=1,2,3...2014
x_n = x_(n+2) for n=1,2,3...2014

Hence,
x_1 = x_3 = x_5 = ... = x_2015 ---- (*)
and x_2 = x_4 = x_6 = ... = x_2016 = 1 - x_1 ---- (**)

From equation (2),
x_1 + x_2 + ... + x_2015 = 0 ---- (#)

Substitute (*) and (**) into #
1008 x_1 + 1007 (1 - x_1) = 0
x_1 + 1007 = 0
x_1 = -1007; 2016年9月4日下午2:03
Herman Yeung 說...: thanks a lot ^^; 2016年9月4日下午2:29

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