# Visualising the sum of the first $n$ positive odd integers [duplicate]

Using the fact that $$1+2+\cdots+n=\frac{n(n+1)}{2}$$, we can deduce that sum of first $$n$$ positive odd integers is $$n^2$$. However, is there a way of finding the sum of $$1+3+5+\cdots+(2n-1)$$ visually?

Imagine wooden cubes stacked in rows, with the basis containing, say, 7cubes, the row above, 5 cubes, the row still above, 3 and the last row $$1$$, like this:
It is a geometrical evidence that, moving the grey squares from the bottom right corner to the top left corner, one recreates a square with sides equal to the number of rows, i.e. 4 units, hence we have $$16$$ of them for the sum of the $$4$$ first odd numbers.