How was the value of e determined
It is determined in many different ways:
1): (1 + 1/n)^n.......as n tends to infinity=2.71828.........etc.
2): 1 + 1/1! + 1/2! +1/3! + 1/4!...............=2.71828.........etc.
I'm not understanding your question :(
Have a look at: https://en.wikipedia.org/wiki/E_(mathematical_constant)