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Limit of sum of inverse of squres

Source: Moldova NMO 2010 problem 4

April 14, 2010
limittrigonometrynumber theory unsolvednumber theory

Problem Statement

Let a_n\equal{}1\plus{}\dfrac1{2^2}\plus{}\dfrac1{3^2}\plus{}\cdots\plus{}\dfrac1{n^2} Find lim⁡n→∞an \lim_{n\to\infty}a_n
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