Mathematical induction_ Basic concepts, Lecture notes of Mathematics

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MATHEMATICAL INDUCTION

INTRODUCTION:-

It is the theoretical topic in mathematics that is basically based on the concept. It is simply defined as a “means of proving a theorem by showing that if it is true of any particular case it is true of the next case in a series, and then showing that it is indeed true in one particular case.” There is no any formula used in this topic we just proved induction by using

our hypothesis (observation). We always proof for (n=k+1) th term , where

“k” belongs to natural numbers as it is replaced by “n”. For e.g. if k=3 then n=3+1= 4 rth so it showed that we proved for the fourth term.

Steps

To solve mathematical induction there are 3 steps which is always followed. Solving Mathematical Induction Questions includes the following steps:

1. Always proof for n=1 ( n belongs to Natural numbers ):- Generally, we have an equation given in which the nth term (Tn) in which is equal to “n” terms. The expression which is on the right- hand side is known as the “n” term and the expression which is on the left- hand side is the “Tn” term.