MATHEMATICAL INDUCTION

Mathematical Induction is a technique for proving general results or theorem involving positive integers.
The word Induction means the method of inferring a general statement from the validity of particular cases.

Statement : A sentence  which can be judged to be true or false is called statement.
It is generally denoted by P(n).

Principle of mathematical Induction

Let P(n) be a statement involving the natural number n. Then
  1. P(1) is true and
  2. P(k+1) is true whenever P(k) is true, then P(n) is true for all natural numbers n.

For proving that statement P(n) holds for all natural numbers n.
Following steps are applied :
  1. Verification that P(n) holds for n = 1 i.e P(1) is true.
  2. Suppose that P(n) holds for every k which belongs to N
  3. Prove that P(n) holds for n = k + 1.
Exercise 4.1
1 Using the Principle of Mathematical Induction Prove that 1 + 3 + 32 +…….+ 3n-1 = (3n – 1)/2 for all natural numbers. 

Sol  

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