Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000

Solution:

By splitting 1.1 and then applying binomial theorem, the first few terms of (1.1)¹⁰⁰⁰⁰ be obtained as

(1.1)¹⁰⁰⁰⁰ = (1 + 0.1)¹⁰⁰⁰⁰

= ¹⁰⁰⁰⁰C₀ + ¹⁰⁰⁰⁰C₁ (0.1) + other positive terms

= 1 + 10000 x (0.1) + other positive terms

= 1 + 1000 + other positive terms

= 1001 + other positive terms

> 1000

Hence, (1.1)¹⁰⁰⁰⁰ > 1000

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 10

Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

Summary:

Using the binomial theorem, (1.1)¹⁰⁰⁰⁰ or 1000 are given to be compared. We have found that (1.1)¹⁰⁰⁰⁰ > 1000