Example 3

Tag 0BTE, permanent. Cite it as [Bourbaki, Tag 0BTE].

Let $a$ and $b$ be two numbers $< 1$ ; then

\frac{1}{a^m + b^n} \leq \frac{1}{2(\sqrt{a})^m (\sqrt{b})^n}

and hence the family

\left( \frac{1}{a^m + b^n} \right)

is summable in

\mathbf{R}

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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