Zaymiey

📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

Mathematical induction is most useful for proving results involving a variable:

Answer: n, a positive integer.

  • A n, a positive integer
  • B x, a real number
  • C z, a complex number
  • D θ, an angle

Correct answer: A. n, a positive integer

Explanation: Induction applies to statements indexed by a positive integer n.

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.

Read the full Principle of Mathematical Induction notes →