Find the remainder when `10^(1) + 10^2 + 10^3 + 10^4 + 10^5 + …….. + 10^(99)` is divided by 6.

Explanation

The remainder when `10^1` is divided by 6 is 4
The remainder when `10^2` is divided by 6 is 4
The remainder when `10^3` is divided by 6 is 4
The remainder when `10^4` is divided by 6 is 4
The remainder when `10^5` is divided by 6 is 4
Thus the requried remainder is always 4.
So, the requried remainder=`4+4+4+...99times/6`=396/6`
Thus the remainder is zero.