Alfred Chern
Reputation
2,248
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
4 12
Impact
~23k people reached

• 0 helpful flags
• 4 votes cast

 18 Prove that a positive polynomial function can be written as the squares of two polynomial functions 8 sum of the series 7 An inequality on trace of product of two matrices 7 Please prove: $\lim_{n\to \infty}\sqrt[n]{\frac{1}{n!}} = 0$ 6 Evaluate integral: $\int_0^{+\infty}\frac{\cos{bx}-\cos{ax}}{x}dx$

### Reputation (2,248)

 +10 Prove $\sqrt[3]{60}>2+\sqrt[3]{7}$ +10 How find this $\lim_{n\to\infty}\frac{1+\sqrt[n]{2}+\sqrt[n]{3}+\cdots+\sqrt[n]{n}}{n}$ +10 How find this limits $\lim_{n\to\infty}\left(\sin{\frac{\ln{2}}{2}}+\sin{\frac{\ln{3}}{3}}+\cdots+\sin{\frac{\ln{n}}{n}}\right)^{1/n}$ +10 An inequality on trace of product of two matrices

### Questions (4)

 1 Prove that $P(x)$ is a polynomial. 1 Generalize Gauss-Bonnet Formula to non-simple closed curves 1 Solution of parabolic PDE system 0 Existence of the derivative

### Tags (61)

 32 real-analysis × 17 24 sequences-and-series × 13 31 calculus × 20 22 polynomials × 3 26 analysis × 6 15 linear-algebra × 10 25 limits × 13 13 algebra-precalculus × 13 25 inequality × 10 12 matrices × 6

### Accounts (6)

 Mathematics 2,248 rep 412 MathOverflow 119 rep 2 Meta Stack Exchange 101 rep Mathematics Educators 101 rep Academia 101 rep