CHAPTER 8

Mathematical Induction and Binomial Theorem

It is a method used to prove simple or complicated statements in Mathematics. Binomial theorem helps in expanding the expression [x + y]n. For proving the statement of the binomial, we make use of this mathematical induction.

8.1  PRINCIPLE OF MATHEMATICAL INDUCTION

It is a method of proving mathematically a given statement for all natural numbers. This proof can be carried over in two steps.

Step 1

Prove the statement for n = 1.

Step 2

It is an inductive step, i.e. assuming the statement for n = m and proving it for n = m + 1.

Then by induction, we consider that the statement is true for any real value of n.

EXAMPLES

  1. Prove that 1 + 2 + 3 + … + [n−1] + n = n[n + 1]/2

    Step 1

    Consider the statement ...

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