My visual interpretation of $1+2+3+ \dots +n$

Question

To be frank, I didn't learn any sort of proof for this (visual or non-visual), so I came up with this proof through trial and error.
Moreover, I haven't checked my proof online yet, therefore I am not sure if I am the first one to come up with this proof - Nonetheless, it is still quite a remarkable proof, at least for me :D.

Hope you will appreciate my visual proof from below!

Answer 1

Not quite visual, but won't this be simpler?

Write:$$S=1+2+3+\dots +(n-1)+n$$ Reciprocate the order of terms: $$S=n+(n-1)+\dots +3+2+1$$ Add both: $$2S=\underbrace{(n+1)+(n+1)+\dots +(n+1)}_{n \text{ times}}$$ $$2S=n\cdot(n+1)$$

$$S=\frac{n\cdot(n+1)}2$$