Siméon
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### Answers (253)

 23 Surprising identities / equations 16 Evaluate $\lim\limits_{n \to\infty} \left(\frac{n-1} {2n+2}\right)^n$ 14 How to prove the inequality between mathematical expectations? 13 Proof of the derivative of $x^n$ 13 What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

### Reputation (8,941)

 +10 How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$? +20 How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4? +5 Problem of limit with binomial coefficients +10 How to find integral of $\int_0^\infty \frac{\ln ^2z} {1+z^2}\mathrm{d}z$?

### Questions (5)

 11 Problem of limit with binomial coefficients 10 Limit of an integral (remainder term of a Euler-Maclaurin expansion) 9 Asymptotic expansion of a series 5 “$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing 5 Value of an integral related to Stirling's formula

### Tags (122)

 132 sequences-and-series × 40 82 probability-theory × 35 112 real-analysis × 44 51 inequality × 16 112 calculus × 36 47 convergence × 18 103 limits × 31 45 measure-theory × 16 90 probability × 44 44 analysis × 11

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