Let { a_k } be any sequence of real numbers that satisfies

   ak ≥ ak+1 > 0 for all k≥1.

Let { r_k } be the sequence of real numbers that satisfies

   rk = ak                        for k = 1,

      = ak*√[ 1 - tk*tk ]          for k > 1,

   where tk = ak/(2*rk-1).

Clearly, for all k > 1, r_k is defined and greater than zero
if t_k∈(0,1).

Prove or disprove that t_k∈(0,1) for all k > 1.

There are no comments yet.