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A4

Part of 1963 Putnam

Problems(1)

Putnam 1963 A4

Source: Putnam 1963

5/1/2022
Let (an)(a_n) be a sequence of positive real numbers. Show that lim sup⁡n→∞n(1+an+1an−1)≥1 \limsup_{n \to \infty} n \left(\frac{1 +a_{n+1}}{a_n } -1 \right) \geq 1 and prove that 11 cannot be replaced by any larger number.
PutnamLimsupSequence