Let the sequence of real numbers { rk } be defined by
rk = ak if k = 1
= ak*[ 1 - ( ak/[ 2*rk-1 ] )2 ] if k > 1.
Prove that { rk } is astrictly monotonically decreasing sequence with
ak > rk > 0 for k > 1,if the sequence of real numbers { ak } is a
monotonically decreasing sequence with
ak > 0 for k ≥ 1.
