Let the sequence of real numbers { r

_{k}} be defined by

**Prove that { r**

r_{k}= a_{k}if k = 1 = a_{k}*[ 1 - ( a_{k}/[ 2*r_{k-1}] )^{2}] if k > 1.

_{k}} is a

strictly monotonically decreasing sequence with

**if the sequence of real numbers { a**

a_{k}> r_{k}> 0 for k > 1,

_{k}} is a

monotonically decreasing sequence with

a_{k}> 0 for k ≥ 1.