Search found 36 matches

by akotronis
Sun Sep 02, 2018 6:04 pm
Forum: Archives
Topic: A Collection Of Problems Published On Mathematical Magazines
Replies: 1
Views: 4586

A Collection Of Problems Published On Mathematical Magazines

A Collection Of Problems Published On Mathematical Magazines.
by akotronis
Sun Sep 02, 2018 6:03 pm
Forum: Archives
Topic: Asymmetry V4 November 2013
Replies: 0
Views: 4016

Asymmetry V4 November 2013

Asymmetry V4 November 2013
by akotronis
Sun Sep 02, 2018 6:02 pm
Forum: Archives
Topic: Asymmetry V3 March 2013
Replies: 0
Views: 2904

Asymmetry V3 March 2013

Asymmetry V3 March 2013
by akotronis
Sun Sep 02, 2018 6:01 pm
Forum: Archives
Topic: Asymmetry V2 January 2013
Replies: 0
Views: 2945

Asymmetry V2 January 2013

Asymmetry V2 January 2013
by akotronis
Sun Sep 02, 2018 6:00 pm
Forum: Archives
Topic: Asymmetry V1 November 2012
Replies: 0
Views: 2825

Asymmetry V1 November 2012

Asymmetry V1 November 2012
by akotronis
Sat Jul 09, 2016 5:49 am
Forum: Analysis
Topic: A trigonometric - logarithmic integral
Replies: 1
Views: 2846

A trigonometric - logarithmic integral

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


NOTE
Proposed by Paolo Perfetti
by akotronis
Thu Jul 07, 2016 4:36 pm
Forum: Real Analysis
Topic: Behaviour near a singular point
Replies: 1
Views: 1975

Behaviour near a singular point

Evaluate \(\displaystyle\lim_{x\to-e^+}\int_{0}^{+\infty}\frac{(x+e)^{1/2}}{e^t+xt}\,dt\), if it exists.
by akotronis
Thu Jul 07, 2016 1:52 pm
Forum: Calculus
Topic: \(\sum_{n\geq1}\frac{1}{(2n-1)(3n-1)(4n-1)}\)
Replies: 3
Views: 3257

Re: \(\sum_{n\geq1}\frac{1}{(2n-1)(3n-1)(4n-1)}\)

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+1)...
by akotronis
Thu Jul 07, 2016 1:50 pm
Forum: Calculus
Topic: \(\sum_{n\geq1}\frac{1}{(2n-1)(3n-1)(4n-1)}\)
Replies: 3
Views: 3257

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

Evaluate \(\displaystyle\sum_{n\geq1}\frac{1}{(2n-1)(3n-1)(4n-1)}\).
by akotronis
Thu Jul 07, 2016 1:44 pm
Forum: Analysis
Topic: A class of alternate infinite series
Replies: 2
Views: 3106

Re: A class of alternate infinite series

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 functio...