Felix Klein

 10 Let $a_n$ be a sequence of real numbers such that $\lim(a_n\sum_{k = 1}^n a_k^2) = 1$ 6 How fast does the sequence $b_{n+1}=b_n+\frac{1}{b_n}$ grow? 6 An integral involving a smooth function 6 Find monotonically increasing function $f$ on $[ 1,+\infty )$ such that $x ( f ( x^{2} ) + 1 ) = f ( x ) ( x^{2}+1 )$? 6 Determine a constant for a certain limit involving arctan function

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### Questions (2)

 3 General cyclic inequality in $n$ variables. 2 The rate of convergence of equidistant Riemann sum of a continuous function.

### Tags (49)

 34 calculus × 9 8 complex-analysis × 6 22 real-analysis × 8 8 inequality × 4 19 sequences-and-series × 6 8 analysis × 3 11 integration × 6 7 linear-algebra × 3 9 functions × 2 7 matrices × 3

### Bookmarks (7)

 28 Bound on the sum of squared distances between points inside a semi-circle 21 A closed form of $\sum_{n=1}^\infty\left[ H_n^2-\left(\ln n+\gamma+\frac1{2n} \right)^2\right]$ 11 prove this nice inequality $\left|\prod_{i=1}^{n}(a_{i}-a_{i+1})\right|\le \frac{3\sqrt{3}}{16}$ 6 Convergent sequence with odd terms decreasing and even terms increasing 4 Examples of $C^1(\mathbb{R}^2)$ functions where mixed partials are equal nowhere