>948
 c = arccosh(a) = log(a+√(a^2 -1)),
とおくと
 a_[n] = cosh(c・2^(n-1)),
 b_[n] = sinh(c・2^(n-1)) /√N,
a_[n]/b_[n] = coth(c・2^(n-1))*√N → √N  (n→∞),