Using binomial theorem, evaluate each of the following: (99)⁵

Solution:

99 can be expressed as the difference of two numbers whose powers are easier to calculate.

Hence, 99 = 100 - 1

Therefore,

(99)⁵= (100 - 1)⁵

Now we will expand this using binomial theorem.

= ⁵C₀ (100)⁵ - ⁵C₁ (100)⁴ (1) + ⁵C₂ (100)³ (1)² - ⁵C₃ (100)² (1)³ + ⁵C₄ (100) (1)⁴ + ⁵C₅ (1)⁵

Here, we can calculate the binomial coefficients ⁵C₀, ⁵C₁, ... using the nCr formula.

= (100)⁵ - 5(100)⁴ + 10 (100)³ - 10 (100)² + 5(100) - 1

= 10000000000 - 500000000 + 10000000 -100000 + 500 - 1

= 10010000500 - 500100001

= 9509900499

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 9

Using binomial theorem, evaluate each of the following: (99)⁵

Summary:

Using binomial theorem, (99)⁵ is given to be evaluated. We have found that it equals 9509900499