On the Head and the Tail of the Colored Jones Polynomial

The colored Jones polynomial is a series of one variable Laurent polynomials
J(K,n) associated with a knot K in 3-space.
We will show that for an alternating knot K the absolute values of
the first and the last three leading coefficients of J(K,n) are
independent of n when n is sufficiently large.
Computation of sample knots indicates that this should be true for any
fixed leading coefficient of the colored Jones polynomial for alternating knots.
As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.

Colored Jones Polynomial, Volume Conjecture, Alternating Knots, Adequate Knots