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📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

In an induction proof of divisibility, the (k + 1) case is handled using the:

Answer: the inductive hypothesis.

  • A the inductive hypothesis
  • B just the base case
  • C a final guessed value
  • D a random chosen number

Correct answer: A. the inductive hypothesis

Explanation: The inductive hypothesis about the k case is rewritten to reveal the divisor in the (k + 1) case.

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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