a) Prove that if x1 > 2 and xn+1 = 1 + xn - 1 for n

Question:

a) Prove that if x1 > 2 and xn+1 = 1 + √xn - 1 for n ∈ N, then 2 < xn+1 < xn holds for all n ∈ N.
b) Prove that if 2 < x1 < 3 and xn+1 = 2 + √xn - 2 for n ∈ N, then 0 < xn < holds for all n ∈ N.
c) Prove that if 0 < x < 1 and xn+1 = 1 - √1 - xn for n ∈ N, then 0 < xn+1 < xn holds for all n ∈ N.
d) Prove that if 3 < x1 < 5 and xn+1 = 2 + √xn - 2, then 3 < xn+1 < xn holds for all n ∈ N.