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find the remainder when 2.2.2........(100 times) +3.3.3....(100 Times) +4.4.4...(100TIMES) +5.5.5....(100 times) is divided by seven

find the remainder when  2.2.2........(100 times) +3.3.3....(100 Times) +4.4.4...(100TIMES) +5.5.5....(100 times) is divided by seven

Grade:

1 Answers

Akash Kumar Dutta
98 Points
8 years ago

222..(100 times)=2+10.2+100.2 .... 10^100.2
=2(1+10+100...10^100)
=2(10^100 - 1)/9
writing all of them in this manner and adding,
we get
(10^100 - 1).(2+3+4+5)/9
=(10^100 - 1).14/9
hence when divided by 7 the remainder is 0.ANS
Plzz approve

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