Excel in math, science, and engineering

\[\large \large \lim_{n\to\infty } \left \lfloor \frac{\Sigma_{r=0}^{n-1} \frac1n f(\frac{r}n) + \Sigma_{r=1}^{n} \frac1n f(\frac{r}n)}{2 \int_0^1f(x) \, dx}\right \rfloor \]

Prove that

\[ \displaystyle \sum_{-\infty}^{\infty} \dfrac1{n+a} = \pi \cot (\pi a ) . \]

On a 3 by 3 grid, the red, yellow, blue and green 2 by 2 squares are placed in some order. They have to be placed in their location (IE ...

What is the smallest positive integer which cannot be formed using the digits 2, 0, 1, 4 in that order? You are allowed to use \( +, -, \times, \div\), exponential, factorials, etc ...

I've been looking at functions \(f:\mathbb{R}^n \to \mathbb{R}\) which necessarily satisfy the following 3 properties. Given \( a_1, a_2, \dots a_n \in \mathbb{R}^+ \)

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