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The sum of cubes of three consecutive natural numbers is divisible by:
- a)2
- b)9
- c)7
- d)5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sum of cubes of three consecutive natural numbers is divisible by:...
n3 + (n+1)3 + (n−1)3
=3(n)3 + 6n
=3n(n2 + 2)
=3n(n2 − 1 + 3)
=3(n(n−1)(n+1)+3n)
n(n−1)(n+1) and 3n are both divisible by 3. Hence their sum is also divisible by 3.
Therefore the whole number is divisible by 9.
=3(n)3 + 6n
=3n(n2 + 2)
=3n(n2 − 1 + 3)
=3(n(n−1)(n+1)+3n)
n(n−1)(n+1) and 3n are both divisible by 3. Hence their sum is also divisible by 3.
Therefore the whole number is divisible by 9.
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Community Answer
The sum of cubes of three consecutive natural numbers is divisible by:...
The answer should be b as if we take the numbers as 1,2,3 they are divisible by 9 and if we take them as 2,3,4 then also they are divisible by 9
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The sum of cubes of three consecutive natural numbers is divisible by:a)2b)9c)7d)5Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sum of cubes of three consecutive natural numbers is divisible by:a)2b)9c)7d)5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of cubes of three consecutive natural numbers is divisible by:a)2b)9c)7d)5Correct answer is option 'A'. Can you explain this answer?.
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