All sequences of $k$ elements $(a_1,a_2,...,a_k)$ are considered, where each $a_i$ belongs to the set $\{1,2,... ,2021\}$. What is the sum of the smallest elements of all these sequences?
Source: Portugal OPM 2021 p3
Tags: combinatorics, number theory, algebra
All sequences of $k$ elements $(a_1,a_2,...,a_k)$ are considered, where each $a_i$ belongs to the set $\{1,2,... ,2021\}$. What is the sum of the smallest elements of all these sequences?