Due to another of his misbehaved, 
the primary school's teacher of the young Gauß,  Herr J.G. Büttner, to keep the bored and unruly young schoolboy Karl Friedrich Gauss busy for a good long time, while he teaching arithmetic to his mates,
assigned him the problem of adding up all the whole numbers from 1 through a given number `n`.
Your task is to help the young Carl Friedrich to solve this problem as quickly as you can; so, he can astonish his teacher and rescue his recreation interval.
Here's, an example:
```
f(n=100) // returns 5050 
```
It's your duty to verify that n is a valid positive integer number. If not, please, return false (None for Python, null for C#).
> **Note:** the goal of this kata is to invite you to think about some 'basic' mathematic formula and how you can do performance optimization on your code. 
> Advanced - experienced users should try to solve it in one line, without loops, or optimizing the code as much as they can.
-----
**Credits:** this kata was inspired by the farzher's kata 'Sum of large ints' . In fact, it can be seen as a sort of prep kata for that one.
def f(n):
    return int((((n**2)-1) + (1+n))/2) if isinstance(n, int) and n > 0 else None
def f(n):
    return int((((n**2)-1) + (1+n))/2) if isinstance(n, int) and n > 0 else None