Question:

1. Prove that for 0 ≤ a b and any integers n ≥ 1, we have
   b ⁿ ((n+1) a –nb) < a ⁿ⁺¹
   Hint: prove first that
   < (n+1) b ⁿ
2. Define now
   a _n =
   Use a = 1 + and b = 1 + to show that a _n is increasing.
3. Use a = 1 and b = 1 + to show that a _n is bounded from above (Hint:
   Note that a _n is increasing, so a _n ≤ a _2n for all n ≥ 1)
4. Conclude that a _n is convergent

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