# Difference between revisions of "2017 AIME I Problems/Problem 3"

## Problem 3

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 $1000$.

## Solution

We see that $d(n)$ appears in cycles of $20$, 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, or $7000$ 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 get that the answer is $\boxed{69}$.