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

Abstract

Motivated by the fundamental presence of mathematics in all engineering and scientific fields, I made this mathematical article in order to answer many of my personal questions which are also not answered questions in mathematics. This is a mathematical article that proves a useful recurrence relation that is very useful for mathematics demonstrations. The article proves also that four infinite series are equivalent. Hence, this article opens new opportunities to demonstrate and develop new mathematical findings and observations. The demonstrated formulas of this article can also be very useful for all the fields that apply mathematics and especially infinite series and sums.