I saw this identity somewhere and I'm wondering if there's a more intuitive explanation for this:
$$\sum_{k=1}^{n} 2k-1 = n^2$$
I know how to verify it algebraically by simplifying the left side but is there another way to think about this? Could the fact that the derivative of $n^2=2n$ has something to do with it? What significance does it have, if any?
