Norbert
Reputation
40,893
96/100 score
6 45 126
Impact
~437k people reached

 32 Infinite product of sine function 29 Evaluating $\lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2}$ 23 Compute the limit of $\frac1{\sqrt{n}}\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)^{1/n^2}$ 21 Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$ 20 Inequality. $a^2+b^2+c^2 \geq a+b+c$

### Reputation (40,893)

 +5 Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? +10 Construct a complete metric on $(0,1)$ +25 Limit of sequence of linear functionals +10 a compact operator on $l^2$ defined by an infinite matrix

### Questions (47)

 73 Continuous projections in $\ell_1$ with norm $>1$ 22 Computing $\lim\limits_{n\to+\infty}n\int_{0}^{\pi/2}xf(x)\cos ^n xdx$ 22 Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? 20 Solving functional equation $f(x)^2+f(y)^2=f(x+y)(f(f(x))+f(y))$ 16 Minmax problem for polygons

### Tags (187)

 1k functional-analysis × 464 264 integration × 58 512 real-analysis × 157 215 limits × 40 472 calculus × 92 204 operator-theory × 95 309 banach-spaces × 136 174 measure-theory × 68 267 sequences-and-series × 57 154 analysis × 60

### Accounts (7)

 Mathematics 40,893 rep 645126 MathOverflow 577 rep 420 TeX - LaTeX 188 rep 7 Stack Overflow 103 rep 3 Academia 101 rep 1