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About a sequence

Source: 2022 China Southeast Grade 10 P1

August 2, 2022
algebraSequenceinduction

Problem Statement

The positive sequence {an}\{a_n\} satisfies:a1=1+2a_1=1+\sqrt 2 and (an−an−1)(an+an−1−2n)=2(n≥2).(a_n-a_{n-1})(a_n+a_{n-1}-2\sqrt n)=2(n\geq 2). (1)Find the general formula of {an}\{a_n\}; (2)Find the set of all the positive integers nn so that ⌊an⌋=2022\lfloor a_n\rfloor=2022.
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