已知数列{An}满足：a1=4，2an+a（n+1）=[（-1）^n]*an*a（n-1），（n≥2，n∈N″

2a(n+1)+a(n) = (-1)^(n+1)a(n+1)a(n),
2/a(n) + 1/a(n+1) = (-1)^(n+1),
1/a(n+1) = -2/a(n) + (-1)^(n+1) ,
1/a(n+1) + (-1)^(n+1) = -2/a(n) + (-2)(-1)^n = (-2)[1/a(n) + (-1)^n],
{1/a(n)+(-1)^n}是首项为1/a(1)+(-1)=-3/4,公比为(-2)的等比数列．
1/a(n) +(-1)^n =(-3/4)(-2)^(n-1),
1/a(n) = 3*2^(n-1)(-1)^n/4 - (-1)^n = [3*2^(n-3) - 1](-1)^n,
a(n) = (-1)^n / [3*2^(n-3) - 1]

b(n)= a(n) sin[(2n-1/2)π] = a(n) sin[-π/2] = -a(n) = (-1)^(n+1)/[3*2^(n-3) - 1 ],
b(2n)=-1/[3*2^(2n-3) - 1],
b(2n-1) = 1/[3*2^(2n-4) - 1],
b(2n-1) + b(2n) = 1/[3*2^(2n-4) - 1] - 1/[3*2^(2n-3) - 1]