ACARCHAU
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 13 Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin…(\sin(x)..)$ 9 limit of the sum $\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}$ 9 Can a symmetric matrix always be represented as the sum of a positive-definite and negative-definite matrix? 9 Summation of $\sum\limits_{n=1}^{\infty} \frac{x(x+1) \cdots (x+n-1)}{y(y+1) \cdots (y+n-1)}$ 8 Measurable function remaining constant

### Reputation (1,941)

 +10 Can a symmetric matrix always be represented as the sum of a positive-definite and negative-definite matrix? +5 sign reversing involution proof of a combinatorial identity +2 heat equation on a surface +5 Matrix with maximal rank in a family of matrices

### Questions (21)

 10 Bell numbers and moments of the Poisson distribution 9 Can this sum be simplified: $\sum_{k=0}^{n-1} { n -1 \choose k } (-2)^{k} (2n - k)!$? 8 Accuracy of approximation to inclusion-exclusion formula in prime sieve 8 sign reversing involution proof of a combinatorial identity 6 Alternative to Ziegler's “Lectures on Polytopes”

### Tags (48)

 44 real-analysis × 15 16 measure-theory × 3 26 limits × 4 15 matrices × 3 25 sequences-and-series × 8 13 numerical-methods 20 analysis × 5 11 summation × 3 18 linear-algebra × 13 10 calculus × 6

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