JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mathematical induction and Divisibility problems

  • question_answer
    For every natural number n, \[n\,({{n}^{2}}-1)\] is divisible by  [RPET 1991]

    A) 4

    B) 6

    C) 10

    D) None of these

    Correct Answer: B

    Solution :

    \[n({{n}^{2}}-1)=(n-1)\,(n)\,(n+1)\] It is product of three consecutive natural numbers, so according to Langrange's theorem it is divisible by 3 ! i.e., 6.


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