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A= 1 101 +2 101 +3 101 + 4 101 +......+34 101 . Find the remainder when A is divided by 70.

A= 1101 +2101 +3101 + 4101 +......+34101. Find the remainder when A is divided by 70.
 

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1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
6 years ago
Hi,

This question can be easily solved by using binomial theorem.
Write 1 as 7-6 two as 7-5 and so on, remember that 7 multiple will be 7 and 8 will be written as 7+1 and so on.

Now when you will apply the BT for (7-1)^101 last term will be -1^101 which will be cancelled by (7+1)^101 s last term.

Similary these pairs will be formed for each of terms which will cancel eaqch other out except for multiples of 7.

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