Maths with David

    9231. FP1. Proof by Induction. Past Exam Questions

    1. November 2025 (9231/12). Question 3
      • The sequence of positive numbers u1, u2, u3, … is such that u1 < 5 and, for n \leq 1 , u_{n+1} = \frac{ 6u_n + 5 }{ u_n + 2 }
        • (a) By considering 5 - u_{n+1} , prove by mathematical induction that un < 5 for all positive integers n. [5 marks]
        • (b) Show that u_{n+1} > u_n for n \geq 1