JEE Main 2020 (Online) 8th January Morning ShiftQuestion 1
The sum $\sum_{k=1}^{20}(1+2+3+\ldots+k)$ is ________.
Sequence and Series · Standard Sums (Σ formulas)
Answer$1540$
Solution
Formulas used. (1) $1+2+\cdots+k=\frac{k(k+1)}{2}$(2) $\sum_{k=1}^{n}\frac{k(k+1)}{2}=\frac{n(n+1)(n+2)}{6}$Step 1 - General term. $1+2+\cdots+k=\dfrac{k(k+1)}{2}$. Step 2 - Sum. $$\sum_{k=1}^{20}\frac{k(k+1)}{2}=\frac{20\cdot21\cdot22}{6}=1540 .$$ Answer: 1540