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Putnam 1950 A3

  • Session A
  1. The sequence x0,x1,x2,…x_{0}, x_{1}, x_{2}, \ldots is defined by the conditions x0=a,x1=b,xn+1=xn−1+(2n−1)xn2n for n≥1,x_{0}=a, x_{1}=b, x_{n+1}=\frac{x_{n-1}+(2 n-1) x_{n}}{2 n} \text { for } n \geq 1, where aa and bb are given numbers. Express lim⁡n−∞xn\lim _{n-\infty} x_{n} concisely in terms of aa and bb.

Dataset text PutnamGAP. Quoted with source.

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