def METHOD_NAME(rate, td, tb, max_k=100, save_to=None):
    """Check that B->0 for k->infty."""
    tau = 1 / rate
    r0 = r_det(td, rate)
    fig = plt.figure()
    for k in range(max_k):
        plt.scatter(k, B(k, r0, td, tb, tau), color="k")
    plt.axhline(0, ls="--", color="k")
    plt.xlabel("$k$")
    plt.ylabel("$B_k$")
    if save_to is not None:
        plt.savefig(save_to)
        plt.close(fig)