Question: Problem 1: Let 0 > a > b. Define

a₁= a, b₁ = b,

and then define inductively

a_n+1 =

for n ≥ 1.

a) Prove that

a_n ≥ a_n+1 ≥ b_n+1 ≥ b_n

for all n ≥ 1 ( Hint prove first that for any

b) Conclude that both a_n and b_n are convergent

c) Call

a^* = and b^* = .

Prove that a^* = b^*