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

For example,
$$X = 1+2+3+4+5+6$$
Then twice $X$ is
$$2X = (1+2+3+4+5+6) + (1+2+3+4+5+6)$$
which we can rearrange as
$$2X = (1+2+3+4+5+6) + (6+5+4+3+2+1)$$
and add term by term to get
$$2X = (1+6)+(2+5)+(3+4)+(4+3)+(5+2)+(6+1)$$
to get
$$2X = 7+7+7+7+7+7 = 6*7 = 42$$
