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nt.number theory - The digits of $\frac{1}{P(n)}$ in base $n+m$ - MathOverflow
$\textbf{Motivation.}$ The purpose of this question is to try to express $\frac{1}{P(n)}$ in base $n+m$ for some monic polynomial $P(x)$. Define $C_k(f(x))$ to...
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Let $a_1, a_2, \ldots$ be a non-increasing sequence of positive numbers such that $\sum_{n \in \mathbb{N}} a_n = \infty$ and let $\varepsilon_1, \varepsilon_2,...
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Consider the sequence $a_n=2^{2n}\binom{2n}n^{-1}$. Stirling's approximation shows that $a_n\sim \sqrt{\pi n}$, thus $$\sum_{n\geq0}\frac{\pi}{2a_n}\qquad...
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