# 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}

= ^{10000}C₀ + ^{10000}C₁ (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