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Hint: If a, b>0 then √a<√ba

(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