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Putnam 2000 A1

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September 6, 2011
PutnamLaTeXfunctioninequalitiesgeometric seriescollege contestsPutnam inequalities

Problem Statement

Let AA be a positive real number. What are the possible values of ∑j=0∞xj2,\displaystyle\sum_{j=0}^{\infty} x_j^2, given that x0,x1,⋯x_0, x_1, \cdots are positive numbers for which ∑j=0∞xj=A\displaystyle\sum_{j=0}^{\infty} x_j = A?
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