Proof that $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$ Why is $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$ $\space$ ?

All these proofs seem very complicated. The way I remember it is:
The sequence is: 1, 2, 3, ..... (n-2), (n-1), n.
Taking the last and first term, 2nd and (n-2)th term and so on, we form n/2 pairs of (n+1). So the sum of n/2 pairs of (n+1) is n/2 * (n+1)
Example: 1, 2, 3, 4, 5, 6
= (1+6) + (2+5) + (3+4)
= 3x7
=21
This still holds for an odd number of terms
