Why is $\sum_\limits{k=1}^{n}\sum_\limits{j=1}^{k}j = \frac12\left(\sum_\limits{k=1}^{n}k^2+\sum_\limits{k=1}^{n}k\right)$

Question

Why is $$\sum_\limits{k=1}^{n}\sum_\limits{j=1}^{k}j = \frac12\left(\sum_\limits{k=1}^{n}k^2+\sum_\limits{k=1}^{n}k\right)?$$

I'm not seeing why they're equivalent. The first expression can be viewed as a half pyramid of some sort, but I don't see what the $k^2$ comes from in the second expression.

Answer 1

HINT

Note that

$$\sum_{j=1}^k j=\frac{k(k+1)}{2}=\frac12 (k^2+k)$$