that the sum of the `$$n^{th}$$ first odd numbers is equal to $$n^2$$.
A odd number $$x$$ can be noted $$2k-1$$. We are looking at $$\sum_{i=1}^{n}(2i - 1)$$.
And we have $$\sum_{i=1}^{n}(-1) = -n$$.
So $$\sum_{i=1}^{n}(2i - 1) = 2\left(\sum_{i=1}^{n}i\right) - n$$
$$= 2 \times \frac{n^2 + n}{2} - n = n^2$$.

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!