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 13 Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin…(\sin(x)..)$ 9 Summation of $\sum\limits_{n=1}^{\infty} \frac{x(x+1) \cdots (x+n-1)}{y(y+1) \cdots (y+n-1)}$ 8 limit of the sum $\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}$ 7 Measurable function remaining constant 7 Can a symmetric matrix always be represented as the sum of a positive-definite and negative-definite matrix?

### Reputation (1,744)

 +10 If $\operatorname{rk}(A) = 1$, when $B + A$ is invertible? +5 sign reversing involution proof of a combinatorial identity +5 well separated points on sphere +10 Prove that the limit exists and then find its limit

### Questions (16)

 9 Can this sum be simplified: $\sum_{k=0}^{n-1} { n -1 \choose k } (-2)^{k} (2n - k)!$? 9 Bell numbers and moments of the Poisson distribution 7 Accuracy of approximation to inclusion-exclusion formula in prime sieve 6 well separated points on sphere 6 sign reversing involution proof of a combinatorial identity

### Tags (44)

 43 real-analysis × 14 15 measure-theory × 3 25 limits × 4 13 matrices × 3 24 sequences-and-series × 6 13 numerical-methods 18 analysis × 4 10 summation × 3 16 linear-algebra × 9 8 calculus × 4

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