algebra precalculus - Why does $1+2+3+cdots+p = {(1⁄2)}cdots(p+1)$

I saw this from Project Euler, problem #1:

If we now also note that $1+2+3+\cdots+p = {(1/2)} \cdot p\cdot(p+1)$

What is the intuitive explanation for this? How would I go about deriving the latter from the former? It has the summation express which I am not sure how to deal with, so unfortunately I am not even sure how I would begin to show these are equivalent.