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📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

The inequality n! > 2ⁿ first becomes true (and stays true) for all n greater than or equal to:

Answer: 4.

  • A 4
  • B 1
  • C 2
  • D 10

Correct answer: A. 4

Explanation: At n = 4, 24 > 16; for n = 3, 6 < 8, so the result holds from n = 4 onward.

Induction as a Domino ChainP(1): base case fallsP(k) knocks down P(k+1)...and so on, foreverBase case = first domino tipped; inductive step = each domino guaranteed to tip the next one

Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.

Concept context

A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.

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