ABSTRACT
Section 1.3 1.3.3. Hint: Write an+1 − an as (an+1 − L)− (an − L). Consider an =
√ n.
1.3.5. Let ε = L+ 12 (1− L). Then, there exists n ∈ N such that, if n ≥ N , an+1 an
≤ L+ ε < 1.
By induction, prove that 0 ≤ aN+k ≤ aN (1 + ε)k. Since the right side goes to 0, we obtain that lim an = 0.
