Task 1. Determine the unit digit of the sum

$$
1+1 \cdot 2+1 \cdot 2 \cdot 3+1 \cdot 2 \cdot 3 \cdot 4+1 \cdot 2 \cdot 3 \cdot 4 \cdot 5+\ldots+1 \cdot 2 \cdot 3 \cdot \ldots \cdot 2017
$$
Solution. In the given sum, all addends, except the first four, have the numbers 2 and 5 as factors. This means that the unit digit of all addends, except the first four, is 0, so the unit digit of the sum coincides with the unit digit of

$$
1+1 \cdot 2+1 \cdot 2 \cdot 3+1 \cdot 2 \cdot 3 \cdot 4=1+2+6+24=33
$$

i.e., it is equal to 3.

## VII section