A-LevelFurther MathematicsProof by InductionMay/June 2015Paper 1 Q37 Marks
The sequence a1, a2, a3, ... is such that a₁ > 5 and an+1 = 4an/5 + 5/an for every positive integer n. Prove by mathematical induction that a„ > 5 for every positive integer n. Prove also that an > an+1 for every positive integer n.
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