神马作文网高二数列题,第十二题选择题,谁有好的快的方法做?
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高二数列题,第十二题选择题,谁有好的快的方法做?
a(n+1)+(-1)^na(n) = 2n-1,
a(2n) + (-1)^(2n-1)a(2n-1) = 2(2n-1)-1, a(2n) - a(2n-1) = 4n-3.
a(2n+1)+(-1)^(2n)a(2n)=2(2n)-1, a(2n+1) + a(2n) = 4n-1,
2 = (4n-1) - (4n-3) = [a(2n+1)+a(2n)] - [a(2n) - a(2n-1)] = a(2n+1) + a(2n-1).
a(2n+1) + a(2n) = 4n-1,
a(2n+2)+(-1)^(2n+1)a(2n+1) = 2(2n+1)-1, a(2n+2) - a(2n+1) = 4n+1,
8n = (4n+1) + (4n-1) = [a(2n+2)-a(2n+1)] + [a(2n+1)+a(2n)] = a(2n+2) + a(2n).
a(2n-1)+a(2n)+a(2n+1)+a(2n+2) = 8n + 2
a(4n-3)+a(4n-2)+a(4n-1)+a(4n) = 8(2n-1) + 2 = 8(2n-2+1) + 2 = 16(n-1) + 10.
a(1)+a(2)+a(3)+a(4)+a(2*4-3)+a(2*4-2)+a(2*4-3)+a(2*4) + ... + a(15*4-3)+a(15*4-2)+a(15*4-1)+a(15*4) = 16*15*(15-1)/2 + 10*15 = 15*(16*7+10) = 15*122 = 1830.
答案：D.
a(2n) + (-1)^(2n-1)a(2n-1) = 2(2n-1)-1, a(2n) - a(2n-1) = 4n-3.
a(2n+1)+(-1)^(2n)a(2n)=2(2n)-1, a(2n+1) + a(2n) = 4n-1,
2 = (4n-1) - (4n-3) = [a(2n+1)+a(2n)] - [a(2n) - a(2n-1)] = a(2n+1) + a(2n-1).
a(2n+1) + a(2n) = 4n-1,
a(2n+2)+(-1)^(2n+1)a(2n+1) = 2(2n+1)-1, a(2n+2) - a(2n+1) = 4n+1,
8n = (4n+1) + (4n-1) = [a(2n+2)-a(2n+1)] + [a(2n+1)+a(2n)] = a(2n+2) + a(2n).
a(2n-1)+a(2n)+a(2n+1)+a(2n+2) = 8n + 2
a(4n-3)+a(4n-2)+a(4n-1)+a(4n) = 8(2n-1) + 2 = 8(2n-2+1) + 2 = 16(n-1) + 10.
a(1)+a(2)+a(3)+a(4)+a(2*4-3)+a(2*4-2)+a(2*4-3)+a(2*4) + ... + a(15*4-3)+a(15*4-2)+a(15*4-1)+a(15*4) = 16*15*(15-1)/2 + 10*15 = 15*(16*7+10) = 15*122 = 1830.
答案：D.