Find the remainder when
10 + 10² + 10³ + 10⁴ + ........ + 10⁹⁹ is divided by 6.

The remainder when 10 is divided by 6 is 4.
The remainder when 10² is divided by 6 is 4.
The remainder when 10³ is divided by 6 is 4.
The remainder when 10⁴ is divided by 6 is 4.
Thus, remainder is always 4.
So, the required remainder,
$$\eqalign{ & = \frac{{4 + 4 + 4 + 4 + \,.....\,99{\text{ times}}}}{6} \cr & = \frac{{396}}{6} \cr} $$
Thus, Required remainder is 0.