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Maths Made Easy TMUA Paper 1 · Q10

Paper 1Logic & proof

Let a1=1a_1=1 and an+1=an+1ana_{n+1}=a_n+\dfrac1{a_n}.

Which statement is true?

Aan<2na_n<\sqrt{2n} for all nn
Ban>2na_n>\sqrt{2n} for all nn
Can=2na_n=\sqrt{2n} for infinitely many nn
Dan<3na_n<\sqrt{3n} for all nn
Ean>2n+1a_n>\sqrt{2n+1} for all nn

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