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

  • question_answer
    Let \[P(n):''{{2}^{n}}<(1\times 2\times 3\times ...\times n)''.\] Then the smallest positive integer for which P(n) is true is

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    [d]  Since \[P(1):2<1\] is false; \[P(2):{{2}^{2}}<1\times 2\] is false \[P(3):{{2}^{3}}<1\times 2\times 3\] is false; \[P(4):{{2}^{4}}<1\times 2\times 3\times 4\] is true


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