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Putnam 1954 A6

Source: Putnam 1954

July 17, 2022
PutnamSequencereal numbers

Problem Statement

Suppose that u0,u1,…u_0 , u_1 ,\ldots is a sequence of real numbers such that un=∑k=1∞un+k2      for  n=0,1,2,…u_n = \sum_{k=1}^{\infty} u_{n+k}^{2}\;\;\; \text{for} \; n=0,1,2,\ldots Prove that if ∑un\sum u_n converges, then uk=0u_k=0 for all kk.
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