30. Find the units digit of $2013^{1}+2013^{2}+2013^{3}+\cdots+2013^{2013}$.
30. Answer: 3
Note that the units digit of $2013^{1}+2013^{2}+2013^{3}+\cdots+2013^{2013}$ is equal to the units digit of the following number
$$
3^{1}+3^{2}+3^{3}+\cdots+3^{2013} \text {. }
$$

Since $3^{2}=9,3^{3}=27,3^{4}=81$, the units digits of the sequence of $3^{1}, 3^{2}, 3^{3}, 3^{4}, \cdots, 3^{2013}$ are
$$
\underbrace{3,9,7,1,3,9,7,1, \cdots, 3,9,7,1}_{2012 \text { numbers }}, 3 .
$$

Furthermore the sum $3+9+7+1$ does not contribute to the units digit, so the answer is 3.