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 42 $L^p$ and $L^q$ space inclusion 41 Contest problem about convergent series 11 Why is $\sum \limits_{k = 0}^{n} (-1)^{k} k\binom{n}{k} = 0$? 10 Computation of limit: $\lim\limits_{n \to \infty} \frac{1}{n}\left ( \cos1+\cos(\frac{1}{2})+\cos(\frac{1}{3}) +…+\cos (\frac{1}{n}) \right )$ 10 Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

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 +10 If $G$ is isomorphic to all non-trivial cyclic subgroups, prove that $G\cong \mathbb{Z}$ or $G\cong \mathbb{Z}_p$ +30 $L^p$ and $L^q$ space inclusion +5 limit of $\frac{f'(x)}{x}$, $f$ convex of class $C^1$ +10 How does this prove AM-GM?

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 22 thoughts about $f(f(x))=e^x$ 9 Probability that two random numbers are coprime 7 There exists a unique function $u\in C^0[-a,a]$ which satisfies this property 7 Prove that a map is continuous 6 Prove that the Lipschitz constant cannot be less than $1$

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 65 inequality × 15 42 lebesgue-integral 51 sequences-and-series × 5 41 contest-math 47 real-analysis × 24 22 binomial-coefficients × 3 44 measure-theory × 5 18 limits × 4 42 lp-spaces 16 linear-algebra × 4

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