# userNaN

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 28 Evaluating $\lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2}$ 23 Infinite product of sine function 21 Compute: $\lim_{n\to\infty}\frac{{\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)}^\frac{1}{n^2}}{\sqrt{n}}$ 19 Inequality. $a^2+b^2+c^2 \geq a+b+c$ 18 if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?

# 36,690 Reputation

 +10 This limit: $\lim_{n \rightarrow \infty} \sqrt [n] {nk \choose n}$. +20 How prove $\frac{2}{3}<\frac{3x^6+15x^2+2}{2x^6+15x^4+3}\le\frac{3}{2}$ +10 Gelfand Topology and C*-algebras +10 Equivalence of cauchy problems

# 46 Questions

 37 Continuous projections in $\ell_1$ with norm $>1$ 19 Computing $\lim\limits_{n\to+\infty}n\int_{0}^{\pi/2}xf(x)\cos ^n xdx$ 17 Solving functional equation $f(x)^2+f(y)^2=f(x+y)(f(f(x))+f(y))$ 15 Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? 15 Minmax problem for polygons

# 178 Tags

 888 functional-analysis × 430 228 banach-spaces × 116 439 real-analysis × 148 190 limits × 39 435 calculus × 90 175 operator-theory × 91 240 integration × 57 150 measure-theory × 65 240 sequences-and-series × 55 138 analysis × 56

# 5 Accounts

 Mathematics 36,690 rep 536109 MathOverflow 354 rep 317 TeX - LaTeX 188 rep 6 Stack Overflow 101 rep 1 Academia 101 rep 1