6. Let n+1 = √3+2n, 20 > 0. Hint: If a, b>0 then √a<√ba<b. (a) Find the fixed point L for which n+1 = n = L. (b) Show algebraically that {n} is increasing, i.e. In ≤In+1 when In € [0, L]. (c) For which zo is {n} bounded above by L? (d) What does the monotone convergence theorem tell you about limn→ In? (e) Write a code to approximate limon when zo = 1 with N = 20 terms. (f) Show that the convergence (sequential rate of convergence) is [at least] linear.

Fig: 1