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Found problems: 1

1963 Putnam, A4
Tags: limsup , sequence
Let $(a_n)$ be a sequence of positive real numbers. Show that $$ \limsup_{n \to \infty} n \left(\frac{1 +a_{n+1}}{a_n } -1 \right) \geq 1$$ and prove that $1$ cannot be replaced by any larger number.