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

Well if we graph the numbers $1,2,3,4,.. $ we get a line. Graphing $(1,1)$, $(2,2)$, $(3,3)$ ...I mean. And these numbers occur in a linear fashion so the average of these numbers from $1$ to $n$ is $\frac{n+1}{2}$ and we multiply that by $n$ numbers. Pretty cool huh?
Maybe this one will interest you too:

$$1+3+5+7+9....+(2n-1)=n^2$$
