The remainder when 40 + 41 + 42 + 43 + ........ + 440 is divided by 17 is:

  • 10
  • 216
  • 34
  • 4None of these
Answer:- 1
Explanation:-

Solution:
Let S be the sum of the expression, Then
S = 40 + 41 + 42 + 43 + ........ + 440
S = (1 + 4 + 16 + 64) + 44 (1 = 4 + 16 + 64) + ...... + 436 + 440
Since, (1 + 4 + 16 + 64) = 85, is divisible by 17. Hence, except 440 remaining expression is divisible by 17.
Thus,
44017(44)101711017

Hence, remainder = 1

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Hence, remainder = 1

", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "
Solution:
Let S be the sum of the expression, Then
S = 40 + 41 + 42 + 43 + ........ + 440
S = (1 + 4 + 16 + 64) + 44 (1 = 4 + 16 + 64) + ...... + 436 + 440
Since, (1 + 4 + 16 + 64) = 85, is divisible by 17. Hence, except 440 remaining expression is divisible by 17.
Thus,
44017(44)101711017

Hence, remainder = 1

", "dateCreated": "7/24/2019 10:09:12 AM" } }
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