olymmath

Putnam 1939 B3

  • Session B
  1. Given the power-series a0+a1x+a2x2+⋯a_{0}+a_{1} x+a_{2} x^{2}+\cdots in which an=(n2+1)3na_{n}=\left(n^{2}+1\right) 3^{n} show that there is a relation of the form an+pan+1+qan+2+ran+3=0a_{n}+p a_{n+1}+q a_{n+2}+r a_{n+3}=0 in which p,q,rp, q, r are constants independent of nn. Find these constants and the sum of the power-series.

Dataset text PutnamGAP. Quoted with source.

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