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Putnam 1952 B5

Source: Putnam 1952

July 7, 2022
PutnamConvergenceseries

Problem Statement

If the terms of a sequence a1,a2,…a_{1}, a_{2}, \ldots are monotonic, and if ∑n=1∞an\sum_{n=1}^{\infty} a_n converges, show that ∑n=1∞n(an−an+1)\sum_{n=1}^{\infty} n(a_{n} -a_{n+1 }) converges.
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