Zaymiey

📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

Assuming the statement is true for n = k is called the ___ hypothesis:

Answer: inductive.

  • A inductive
  • B the base
  • C the final
  • D the random

Correct answer: A. inductive

Explanation: The inductive hypothesis is the assumption that P(k) holds.

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 →