Question 69
Let $a$ be a strictly positive real number and $n \geqslant 1$ an integer. Prove that
$$
\frac{a^{n}}{1+a+\ldots+a^{2 n}} \lt \frac{1}{2 n}
$$
$$
\frac{a^{n}}{1+a+\ldots+a^{2 n}} \lt \frac{1}{2 n}
$$
MathNet 2022-part-02 — 197 problems (EN–VI) Question 69
Math Olympiad Vault · MathNet 2022-part-02 — 197 problems (EN–VI)