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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mock Test - Principle of Mathematical Induction

  • question_answer
    If \[p(n)={{n}^{3}}+{{(n+1)}^{3}}+{{(n+2)}^{3}}\]where \[n\in N\]then p(n) is divisible by

    A) 9     

    B) 7

    C) 13                   

    D) 15

    Correct Answer: A

    Solution :

    [a] Let n=1, \[\therefore P(1)=1+8+27=36\] \[\therefore P(1)=36\] is divisible by 9


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