Just to offer an alternative approach.From equation (1),x_2 = 1 - x_1Also,x_n + x_(n+1) = x_(n+1) + x_(n+2) for n=1,2,3...2014x_n = x_(n+2) for n=1,2,3...2014Hence,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) = 0x_1 + 1007 = 0x_1 = -1007
thanks a lot ^^
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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
thanks a lot ^^
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