Answer
$1+2+3+\displaystyle \cdots+20=\sum_{k=1}^{20}k$
Work Step by Step
$1+2+3+\cdots+20=$
There are 20 terms, count them with index k: $\displaystyle \sum_{k=1}^{20}$(...)
The first term (when k=1) is 1,
The second term (when k=2) is 2,
The kth is k so
$1+2+3+\displaystyle \cdots+20=\sum_{k=1}^{20}k$
