introduction: introduction In algebra or in any other discipline of mathematics, there are certain results or statements that are formulated in terms of n , where n is a positive integer . To prove such statements well-suited principle that is used based on the specific technique is known as the principle of mathematical induction.
Principle of mathematical induction: Principle of mathematical induction Suppose there is a given statement P(n) involving the natural number n such that The statement is true for n=1, i.e. P(1) is true and If the statement is true for n=k(where k is some positive integer), then the statement is also true for n=k+1, i.e. truth of P(k) implies the truth of P(k+1). Then, P(n) is true for all natural numbers n.
Some typical types of statements to be proved by using p.m.i.: Some typical types of statements to be proved by using p.m.i .
HOW TO SOLVE TYPE I PROBLEMS: HOW TO SOLVE TYPE I PROBLEMS
HOW TO SOLVE STATEMENTS CONTAINING SIGNS OF INEQUALITIES: HOW TO SOLVE STATEMENTS CONTAINING SIGNS OF INEQUALITIES
HOW TO SOLVE TYPE III PROBLEMS: HOW TO SOLVE TYPE III PROBLEMS
Slide 11: Presented by adrita kundu class – xi a