# All Questions

58 questions
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### Closed form expression or asymptotic expansion for (periodic) generalized harmonic numbers?

In contrast with the series $\sum_{k=1}^n k$ and $\sum_{k=1}^n1$, there does not (as far as I know) exist a pure closed form expression (or a nice asymptotic expansion other than the Euler-Maclaurin ...
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### Difference between Bernoulli random variables

Given are $n$ independent Bernoulli random variables with parameters $p_1,\dots,p_n$. We want to split them into two parts so as to minimize the expectation $\mathbb{E}[|X-Y|]$, where $X$ is the sum ...
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### How to calculate quantity of Hamilton cycles

If I have $n^2$ vertices and each vertex is adjacent to $2n-2$ vertices, how may I calculate the quantity of possible Hamilton cycles? Would I need to modify the computation if I stipulated that I'm ...
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### Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$

Here is problem: $$\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x$$ The solution I presented in the picture below was made by a Mathematics Teacher I tried to solve this Limit ...