Looking back and ahead

I am back in Ranchi.
It was in November 2010, that I made the blog Measuring Behaviour. During those times I managed to express pi approximately as 22/7. I also had expressions on the mathematical constant e. Frankly there were two things that I wondered. 2n and n. World is unfair(n). World is fair(n). And you measured the behaviour(2n). Gradually I started expressing better. I made a few infinite series expressions. And currently I am with the book "Theory of Complex Functions". Hoping to learn the methods and lemmas.
Later, I realised you have to consider unfair(n) and fair(n) together for measuring behaviour(2n). Expressing in terms of infinite expression, I got

Later I fine tuned and got better pi expressions. These are

I later realised that comb(2n,n) is great in expressions of irrational numbers too. I got

Since I got root 5, I expressed the most famous golden ratio. This what I got

Now. As I wrote above, unfair(n), fair(n), measuring behaviour(2n) is important. But one cannot deny that one looks at the world with only one thing in mind. Either fair. Or unfair. Is it not?
So I tried n and 2n. This is what I got

This has opened a new world to me. For one when dealing with n and 2n and not n,n and 2n, you get an expression which has both pi and e terms. In one expression you have both pi and e in the numerator and in the other(alternated negatives) you get pi in the numerator and e in the denominator.
This gives a lot of insight into the behaviour of a man. If he looks at the world as unfair or fair (one of these) he gets an equation which is absolutely different from if he looks at the world as both fair and unfair, both together.
I am also pasting the definition of error function (of Carl Friedrich Gauss) and that of imaginary error function too.