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why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$
Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$
Dropping the “positive” and “decreasing” conditions in the integral test
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
An arctan integral $\int_0^{\infty } \frac{\arctan(x)}{x \left(x^2+1\right)^5} \, dx$
Can this product be written so that symmetry is manifest?
Proof by contradiction: $ S \subseteq \emptyset \rightarrow S= \emptyset $
Products and coproducts in the simplex category
Number of even and odd subsets
Proof that there is no Banach-Tarski paradox in $\Bbb R^2$ using finitely additive invariant set functions?
Can there be a function that's even and odd at the same time?
Proof for power functions
Inverse of a Positive Definite
Solve by induction: $n!>(n/e)^n$
How do people come up with difficult math Olympiad questions?