Top network posts

• 12 Show $\frac{\sin x_1\sin x_2\cdots\sin x_n}{\sin(x_1+x_2)\sin(x_2+x_3)\cdots\sin(x_n+x_1)}\le\frac{\sin^n(\pi/n)}{\sin^n(2\pi/n)}$, for $\sum x_i=\pi$
• 9 A closed form for $\int_0^\pi \lvert \sin(m t) \cos(n t) \rvert \, \mathrm{d} t$
• 8 The limit and asymptotic analysis of $a_n^2 - n$ from $a_{n+1} = \frac{a_n}{n} + \frac{n}{a_n}$
• 7 How do I evaluate $\sum_{k = 1}^{\infty}\big[\frac{(-1)^{k - 1}}{k}\sum_{n = 0}^{\infty}\big\{\frac{1}{k(2^n) + 1}\big\}\big]$?
• 6 A problem from the Shortlist of the Romanian Mathematics Olympiad
• 6 Find this integral $I=\int\frac{x}{(1-3x)^{3/2}(x+1)^{3/2}}dx$
• 6 Evaluate $\lim_{n\to\infty} \prod_{k=1}^n \frac{2k}{2k-1}\int_{-1}^{\infty} \frac{{\left(\cos{x}\right)}^{2n}}{2^x} \; dx$
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