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CMO 1975 Problem 2

  • Paper

A sequence of numbers a1,a2,a3,...a_1, a_2, a_3, ... satisfies

(i) a1=12a_1 = \frac{1}{2} (ii) a1+a2+⋯+an=n2an (n≥1)a_1+a_2 + \cdots + a_n = n^2 a_n \ (n \geq 1)

Determine the value of an (n≥1)a_n \ (n \geq 1) .

Dataset text AI-MO AoPS. Quoted with source.

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