Doubt about series - which series is this?

I really can't remember (if I have ever known this): which series is this and how to demonstrate its solution?

$$\sum\limits_{i=1}^n i = \frac{n(n+1)}{2}$$

Answer

This is an Arithmetic Series starting from $1$ with difference $1$.

$$\sum\limits_{i=1}^n i = 1 + 2 + 3 + 4 + ... +n = {n (n+1) \over 2}$$
1#Check this out.
2#There's one another related one.