mathimatikoi.org

A Collection Of Problems Published On Mathematical Magazines.

Asymmetry V4 November 2013

Asymmetry V3 March 2013

Asymmetry V2 January 2013

Asymmetry V1 November 2012

Evaluate \(\displaystyle\int_{0}^{\pi/2}4\,\cos^2x\,\ln^2(\cos x)\,dx\).

Evaluate \(\displaystyle\lim_{x\to-e^+}\int_{0}^{+\infty}\frac{(x+e)^{1/2}}{e^t+xt}\,dt\), if it exists.

Thank you Demetres. There is a somewhat general method dealing with sums of fractions with a product as denominator whose number of factors depends on a parameter \(k\).

Using this method, one can show for example, as a generalization of this problem, that

\[\displaystyle\sum_{n\geq1}\frac{1}{(2n ...

Evaluate \(\displaystyle\sum_{n\geq1}\frac{1}{(2n-1)(3n-1)(4n-1)}\).

Nice solution. This problem is I generalization of problem 158 ( http://people.missouristate.edu/lesreid/Adv158.html ) I sent to Missouri State University Problem Corner. Here is my approach:

Using the notation \(\Gamma(k+1)=k!\) for \(k\in\mathbb{N}\cup\{0\}\), where \(\Gamma\) is the Gamma ...