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14 Answers

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10	Sum inequality: $\sum_{k=1}^n \frac{\sin k}{k} \le \pi-1$
6	How to prove that $\int_0^1\left(\sum_{k=n}^\infty {x^k\over k}\right)^2\,dx = \int_0^1 2x^{n-1}\log\left(1+{1\over\sqrt{x}}\right)\,dx.$
5	Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$
4	Two curious “identities” on $x^x$,$e$,and $\pi$
2	An Inequality problem relating $\prod\limits^n(1+a_i^2)$ and $\sum\limits^n a_i$

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833 Reputation

+10	Large Intersection Multiplicity
+10	Two curious “identities” on $x^x$,$e$,and $\pi$
+15	sum of three cubes and parametric solutions
+10	Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$

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7 Questions

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50	Two curious “identities” on $x^x$,$e$,and $\pi$
5	Root of a special polynomial
4	Sphere Covering Problem
3	sum of three cubes and parametric solutions
2	Large Intersection Multiplicity

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26 Tags

19 real-analysis × 4	6 homework × 2
14 inequality × 4	4 gamma-function × 2
12 sequences-and-series × 2	4 calculus × 2
10 integral × 3	2 polynomials × 2
7 limit × 2	2 roots × 2

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