Proof by Induction

The method of mathematical induction is used to prove mathematical statements related to the set of all natural numbers. For the concept of induction, we refer to our page “an introduction to mathematical induction“. One has to go through the following steps to prove theorems, formulas, etc by mathematical induction. Steps of Induction Proofs by … Read more

Important Questions of Mathematical Induction

In this section, we will discuss a few important questions and answers of mathematical induction. For more details of induction, we refer to our page “an introduction to mathematical induction” Problem 1: Prove that $n<2^n.$ Solution: Let P(n) denote the statement $n<2^n.$ Base case: Note that 1 < 21. So P(1) is true. Induction hypothesis: … Read more

Mathematical Induction: Definition, Principles, Solved Examples

Mathematical induction is one of the main tools to prove various mathematical formulas, inequalities, and theorems. In this section, we will discuss the basic concept of mathematical induction. What is Mathematical Induction Mathematical induction is a special technique to prove many mathematical statements usually related to the set of all natural numbers. The technique involves … Read more