Prove that $\overline{e^{ix}}=e^{-ix}$

Determine : $\lim _{n \rightarrow \infty} \left[\frac{1 \cdot 1 !+2 \cdot 2 !+\cdots+n \cdot n !}{(n+1) !}\right]^{(n+1)!}$

How would you define $>$ and $<$ on $\mathbb{C}$?

Prove that $\frac{a^{2}+1}{b}+\frac{b^{2}+1}{a} \geq 4$

How Many 4-Digit Positive Even Numbers Use Only Digits 0 Through 4, With No Digits Repeating?

Permutations of race positions

Hard problems solving tricks

Looking for analytical proof that this function given as a power series is constant.

Every ring homomorphism to the integers is surjective?

Minimum of $\left|1-\left(ab+bc+ca\right)\right|+\left|1-abc\right|$

$\lim\limits_{n\to\infty}n\big(\sum_{k=1}^n\frac{k^2}{n^3+kn}-\frac{1}{3}\big)$?

Which "known" ring is $K = \frac{\mathbb{Z}_5[X,Y]}{(Y-X^2, XY + Y + 2)}$ isomorphic to?

The Automorphism Group $\Gamma(\mathbb{Q}(\sqrt[n]{2}):\mathbb{Q})$ is trivial if $n$ is odd.

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