(Solution) - A Use Theorem 2 4 to show that the sequence defined -(2025 Original AI-Free Solution)

Paper Details

a. Use Theorem 2.4 to show that the sequence defined by
xn = 1/2xn?1 + 1/xn?1 , for n ? 1,
converges to?2 whenever x0 >?2.
b. Use the fact that 0 < (x0??2)2 whenever x0 ??2 to show that if 0 < x0 ?2.
c. Use the results of parts (a) and (b) to show that the sequence in (a) converges to?2 whenever x0 > 0.