Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.5 National olympiad Prove it

Example 4 Let the sequence of non-negative numbers $a_{1}, a_{2}, \cdots$ satisfy the condition: $a_{m+n} \leqslant a_{n}+a_{m}, m, n \in \mathbf{N}_{+}$ , prove that for any positive integer $n$ , we have $a_{n} \leqslant m a_{1}+\left(\frac{n}{m}-1\right) a_{m}$ .

Solution

None

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