1.

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

Answer»

Solution :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.


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