The sum _k=1^20(1+2+3++k) is ________.

Question

The sum $\displaystyle\sum_{k=1}^{20}(1+2+3+\cdots+k)$ is \_\_\_\_\_\_\_\_.

Answer: 1540

Accepted Answer

$$\sum_{k=1}^{20}\frac{k(k+1)}{2} = \frac12\left[\frac{20\times21\times41}{6}+\frac{20\times21}{2}\right] = \frac{2870+210}{2} = 1540.$$

Solutions · 1