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📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

Which kind of result is proved most naturally by mathematical induction?

Answer: a summation formula over n terms.

  • A a summation formula over n terms
  • B the value of a single number
  • C a geometric construction result
  • D the value of a certain limit

Correct answer: A. a summation formula over n terms

Explanation: Induction is ideal for statements about a formula that depends on 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 →