Jagat Singh

In this course, the educator discusses the principles of mathematical induction. The course will be beneficial for IIT JEE Aspirants.

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IIT JEE

JEE Main and Advanced Preparation

English

Principal of Mathematical Induction PMI: IIT JEE

Mathematical Induction

Algebra

Mathematics

IITJEE, NEET UG and Foundation

Ace the toughest competitive and government exams in India 

Test Preparation

Mathematical induction is a mathematical proof technique. It is essentially used to prove that a property P(n) holds for every natural number n, i.e. for n = 0, 1, 2, 3, and so on. Metaphors can be informally used to understand the concept of mathematical induction, such as the metaphor of falling dominoes or climbing a ladder:

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

— Concrete Mathematics

The method of induction requires two cases to be proved. The first case, called the base case (or, sometimes, the basis), proves that the property holds for the number 0. The second case, called the induction step, proves that, if the property holds for one natural number n, then it holds for the next natural number n + 1. These two steps establish the property P(n) for every natural number n = 0, 1, 2, 3, ... The base step need not begin with zero. Often it begins with the number one, and it can begin with any natural number, establishing the truth of the property for all natural numbers greater than or equal to the starting number.

The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction, in some form, is the foundation of all correctness proofs for computer programs

Course overview

Validation of a formula by principal of mathematical induction for IIT JEE and also important for Board exams. Proof of sum of natural numbers, sum of sauares of natural numbers , sum of cubes of natural numbers nad much more.
Basic step, Inductive step, proof for any natural number

Type I

Validation of inequality problems fo any natural number n by using PMI. Technique number 2 or type 2 with basic step, inductive step and proof for natural numbers in case of inequality. Like n+7 <(n+3)^2 and much more

Type II

Problems involving proof for multiple and factors of a given term for natural number n. 3rd type for PMI.
Like to show that x^2n-y^2n is multiple of  (or divisible by) x+y by PMI

Type III

One of the best creative use for mathematical induction for ODD PIE FIGHT and cases where PMI fails with reasons of failures

Creative use and Failures of PMI

A game-changer in Mathematics, produced 100 percentilers multiple times, AIR 33 & 34 (Mains 2024), his courses are the Benchmark for IIT JEE

Vineet Loomba

This course aims to impart all the necessary concepts to score full marks in Mathematical Reasoning portion of JEE Main Exam

(Hindi) Mathematical Reasoning (100% Success)

This course aims to clear all concepts involved in the chapter of Principle of Mathematical Induction

(Hindi) Principle of Mathematical Induction - IIT JEE

Ashish Bajpai

This course will help in understanding Mathematical Induction. The Students will learn Induction technique by use of lot of practice Problems. This course is designed in such a way that beginner can understand the concept easily. The Course starts from simple examples and moves step by step towards complex problems.

(Hindi) Mastering Mathematical Induction

In this course, the educator discusses the principles of mathematical induction. 
The course will be beneficial for IIT JEE Aspirants.

(Hindi) Principals of Mathematical Induction: IIT JEE

teaching experience of more than 5 years . 
Youtube channel -success graph 
 working as maths tutor at success graph education point

Sheenam Sachdeva

Principal of Mathematical Induction chapter 4 from NCERT

(Hindi) Principal of Mathematical Induction

This courses gives and easy to understand knowledge of logarithms and its properties, graphs, logarithmic equations, logarithmic inequations etc. This course is sufficient to cover logarithm part of jee main and advanced preparation. It has numerous solved examples and previous year questions to give learners a strong hold on logarithm portion of IIT-JEE preparation.

Lessons

5 lessons • 59m

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Course overview

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Type I

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Type II

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Type III

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Creative use and Failures of PMI