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

  • question_answer
    If \[P(n):''{{46}^{n}}+{{19}^{n}}+k\] is divisible by 64 for\[n\in N\]? is true, then the least negative integer value of k is.

    A) -1

    B) 1

    C) 2

    D) -2

    Correct Answer: A

    Solution :

    [a] For \[n=1,\]\[P(1):65+k\] is divisible by 64. Thus k, should be -1 Since \[65-1=64\] is divisible by 64.


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