A new equation of four infinite series and sums byusing a generalized recurrence relation

Abstract

Motivated by the fundamental presence of mathematics in all engineering and scientific fields, I made thismathematical article in order to answer many of my personal questions which are also not answeredquestions in mathematics. This is a mathematical article that proves a useful recurrence relation that is veryuseful for mathematics demonstrations. The article proves also that four infinite series are equivalent and thisresult has been tested successfully on the softwares: «GEOGEBRA» and «MATLAB». Hence, this articleopens new opportunities to demonstrate and develop new mathematical findings and observations. Thedemonstrated formulas of this article can also be very useful for all the fields that apply mathematics andespecially infinite series and sums.