# Binomial Theorem

Statement:

where n is a positive integer.

Proof of this theorem is done by mathematical induction

Proof:

[Note:
a) The alternate terms are negative

b) The sign of the last term depends on the value of n.]

Remark: Even though binomial theorem can be applied for negative integral indices and rational indices [with same conditions attached] we are not dealing with those situations in this chapter.

Example 1: Find the expansion of

Solution:

Example 2:
Simplify using binomial theorem

Solution:

Example 3:
Find the value of power of 11, using binomial theorem.

Solution: