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📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

The sum of the first n odd numbers, 1 + 3 + … + (2n − 1), equals:

Answer: n².

  • A
  • B n(n + 1)
  • C 2n
  • D

Correct answer: A. n²

Explanation: The sum of the first n odd numbers is n².

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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