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

  • question_answer
    If \[p(n)={{n}^{2}}+n,\]\[\forall \,n\in N\], then p(n) is

    A) even positive integer

    B) prime number

    C) odd integer

    D)  multiple of 4

    Correct Answer: A

    Solution :

    [a] \[P(n)={{n}^{2}}+n:\]
    \[P(1)=1+1=2;\]
    \[P(2)={{2}^{2}}+2=6;\]
    \[P(3)={{3}^{2}}+3=12\]
    We observe that \[\forall n\in N,\]\[P(n)\] is always an even positive integer.


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