Comparing totals

Can you work out the solution to this tricky summation problem?

Problem



The positive integer $n$ is between $1$ and $20$.

Milly adds up all the integers from $1$ to $n$ inclusive.

Billy adds up all the integers from $n+1$ to $20$ inclusive.

Their totalsĀ are the same.

What is the value of $n$?

This problem is taken from the UKMT Mathematical Challenges.