hi Mitchell

Welcome to the forum.

Known as the sum of counting numbers (or triangle numbers) formula, what you want is:

The diagram below shows where it comes from.

If you stack up n then n-1, then n-2 ....... 3, 2, 1 squares it makes a sort of right angled triangle.

Then make the same again but turn this stack up-side-down and slot it into the triangle to make a rectangle.

The rectangle is 'n' high and n+1 wide so its area is n(n+1).

But we've made twice the sum you want, so divide by 2.

That's it.

Bob