作业帮数列{a（n）}中,a（n+1）+（-1）ⁿ×a（n）=2n-1,则前20项和为——.（麻烦写出过程!）选项：A.76 B.78 C.80 D.82
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数列{a（n）}中,a（n+1）+（-1）ⁿ×a（n）=2n-1,则前20项和为——.（麻烦写出过程!）选项：A.76 B.78 C.80 D.82
数列{a（n）}中,a（n+1）+（-1）ⁿ×a（n）=2n-1,则前20项和为——.（麻烦写出过程!）
选项：A.76 B.78 C.80 D.82
数列{a（n）}中,a（n+1）+（-1）ⁿ×a（n）=2n-1,则前20项和为——.（麻烦写出过程!）选项：A.76 B.78 C.80 D.82
a(2n+1)+(-1)^(2n)a(2n) = 2(2n)-1 = 4n-1 = a(2n+1) + a(2n),
a(2n-1+1)+(-1)^(2n-1)a(2n-1) = 2(2n-1)-1 = 4n-3 = a(2n) - a(2n-1),
(4n-1) - (4n-3) = 2 = [a(2n+1)+a(2n)] - [a(2n)-a(2n-1)] = a(2n+1) + a(2n-1),
2 = a(2n+1) + a(2n-1),
2 = a(4n-1) + a(4n-3).
a(2n+1+1)+(-1)^(2n+1)a(2n+1) = 2(2n+1) - 1 = 4n+1 = a(2n+2) - a(2n+1),
(4n+1)+(4n-1) = [a(2n+2)-a(2n+1)] + [a(2n+1)+a(2n)]=a(2n+2)+a(2n) = 8n,
a(4n)+a(4n-2) = a[2(2n-1)+2] + a[2(2n-1)] = 8(2n-1) = 16n - 8 - 8 +8 = 16(n-1) + 8,
a(4n-3)+a(4n-2)+a(4n-1)+a(4n) = 16(n-1) + 8 + 2 = 16(n-1) + 10,
a(1)+a(2)+...+a(19)+a(20)
=[a(1) + a(2) + a(3) + a(4)] + [a(4*2-3)+a(4*2-2)+a(4*2-3)+a(4*2)]+...+[a(4*5-3)+a(4*5-2)+a(4*5-1)+a(4*5)]
=16(0+1+2+3+4) + 10*5
=16*10 + 5*10
=(16+5)*10
=210