# Find an approximation of (0.99)5 using the first three terms of its expansion.

(0.99)5 = (1 - 0.01)5

We know that-

Hence

= a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

Thus, (a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

Putting a = 1 & b = -0.01, we get-

(1 + (-0.01))5 = (1)5 + 5(1)4(-0.01) + 10(1)3(-0.01)2 + 10(1)2(-0.01)3 + 5(1)(-0.01)4 + (-0.01)5

Using first three terms,

(0.99)5 = (1)5 + 5(1)4(-0.01) + 10(1)3(-0.01)2

= 1 - 0.05 + 0.001

= 1.001 - 0.050

= 0.951

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Greatest term in binomial expansion | Revising Binomial theorem43 mins
Finding remainder using binomial theorem43 mins
Quiz on Greatest term in binomial expansion | Revising Binomial theorem38 mins
Binomial theorem for any index | Interactive Quiz48 mins
Finding coefficient of x^n in binomial expansion59 mins
Interactive Quiz | general & middle terms53 mins
Learn Binomial Theorem through Questions | Check Yourself46 mins
Interactive Quiz on Binomial Theorem40 mins
Lecture on properties of Binomial Coefficients58 mins
Interactive Quiz on properties of Binomial Coefficients51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses