This course teaches mathematical induction, the method for proving a statement for every natural number at once. You start with the principle of finite induction and the stronger principle of complete induction, and learn the standard way to set out a proof. You then collect the standard sums of natural numbers, squares, cubes, fourth powers, odd and even numbers, recall A.P., G.P. and A.G.P. formulas, and learn to find general terms. The final lesson applies induction to divisibility, shows how to find the divisor with a G.C.D., lists standard results and introduces congruence notation.
Intermediate 1st Year Mathematics
Maths 1A: Mathematical Induction
The principle of mathematical induction and how to use it to prove sums, series formulas and divisibility results for every natural number.
- Class 11
- State Board
- 4 lessons
- Quiz included
Overview
Lessons
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The principle of mathematical induction
The principles of finite and complete induction, the base and inductive steps, and how to write a proof by induction for a sum.
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Standard sums
Sums of natural numbers, squares, cubes and fourth powers, of odd and even numbers and their squares and cubes, and the alternating sum 1² − 2² + 3² − …
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Series and general terms
A.P., G.P. and A.G.P. formulas, finding the nth term from differences, and choosing the starting value of n when verifying a formula.
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Divisibility by induction
Finding a divisor with the G.C.D. of two values, proving divisibility by induction, standard divisibility results and congruence modulo m.
Practice papers
Ten question papers that follow the lessons in order. Each has 20 questions for 50 marks (1 hour 30 minutes), with a key sheet and worked solutions.
MCQ tests
Ten tests of 25 multiple-choice questions (30 minutes each). Answer them on the page and check your score, or download the PDF with its key and solutions.
Class notes
Maths 1A: Mathematical Induction (theory notes)
The chapter's theory notes in one PDF, 4 pages.
Download the notes (PDF, 447.8 KB)Test yourself
Maths 1A: Mathematical Induction, Course Quiz
Ten questions across the whole chapter, from the steps of an induction proof to standard sums, series and divisibility. Pick one answer for each.
10 questions, 20 minutes, pass mark 60%.
Take the quiz