Question 11
Evaluate
$\left(\frac12+\frac13+\cdots+\frac1{20}\right)+\left(\frac23+\frac24+\cdots+\frac2{20}\right)$
$+\left(\frac34+\frac35+\cdots+\frac3{20}\right)+\cdots+\left(\frac{18}{19}+\frac{18}{20}\right)+\left(\frac{19}{20}\right).$
**Editorial note for this self-study exercise:** Every fraction i/j with whole numbers 1 ≤ i < j ≤ 20 occurs once. Enter an exact decimal or fraction; do not round.
$\left(\frac12+\frac13+\cdots+\frac1{20}\right)+\left(\frac23+\frac24+\cdots+\frac2{20}\right)$
$+\left(\frac34+\frac35+\cdots+\frac3{20}\right)+\cdots+\left(\frac{18}{19}+\frac{18}{20}\right)+\left(\frac{19}{20}\right).$
**Editorial note for this self-study exercise:** Every fraction i/j with whole numbers 1 ≤ i < j ≤ 20 occurs once. Enter an exact decimal or fraction; do not round.