How to prove $\sum_{i=1}^{n} i = \frac{n}{2}(n+1)$ without words?

Question

Possible Duplicate:
Proof for formula for sum of sequence $1+2+3+\ldots+n$?

Is there a picture proof for $\sum_{i=1}^{n} i = \frac{n}{2}(n+1)$?

Answer 1

Draw an $n$ by $n+1$ rectangular array of lattice points, and split it into two equal halves along an almost diagonal. Taking $n=4$ or $n=5$ is probably good enough.

Or else, equivalently, take an $n+1$ by $n+1$ square array of dots, and erase the main Northwest to Southeast diagonal. Then slide the points of the lower remaining half up by $1$.

Remark: Logically speaking, this cannot be an acceptable answer! A request for a proof without words has been answered by using $\dots$ words.