For a positive integer $n$, let $d_n$ be the units digit of $1 + 2 + \dots + n$. Find the remainder when
\[\sum_{n=1}^{2017} d_n\]is divided by $1000$.
We see that $d_n$ appears in cycles of $20$ and the cycles are \[1,3,6,0,5,1,8,6,5,5,6,8,1,5,0,6,3,1,0,0,\] adding a total of $70$ each cycle.
Since $\left\lfloor\frac{2017}{20}\right\rfloor=100$, we know that by $2017$, there have been $100$ cycles and $7000$ has been added. This can be discarded as we're just looking for the last three digits.
Adding up the first $17$ of the cycle of $20$, we can see that the answer is $\boxed{069}$.

~ Maths_Is_Hard