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The sum $\sum_{k=1}^{20}(1 + 2 + 3 + \ldots + k)$ is _______.
Given series can be written as
$\sum_{k=1}^{20}\frac{k(k+1)}{2} = \frac{1}{2}\sum_{k=1}^{20}(k^2 + k)$
$= \frac{1}{2}\left[\frac{20(21)(41)}{6} + \frac{20 \times 21}{2}\right] = \frac{1}{2}[2870 + 210] = 1540$
BETA
