Question

The sum \(\displaystyle\sum_{k=1}^{20} (1 + 2 + 3 + \ldots + k)\) is :

Hint:

Replace the inner sum by k(k+1)/2 and use the standard sums of k and k^2.

Answer 1

Correct Answer: 1540

\(1+2+\ldots+k = \frac{k(k+1)}{2}\).
Sum \(= \frac{1}{2}\left(\sum k^2 + \sum k\right)\) for k = 1 to 20.
\(\sum k^2 = \frac{20\cdot21\cdot41}{6} = 2870\), \(\sum k = \frac{20\cdot21}{2} = 210\).
Sum \(= \frac{2870 + 210}{2} = 1540\).
Answer: 1540