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

Question

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

Sum

Solution

By splitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)¹⁰⁰⁰⁰ can be obtained as

(1.1)¹⁰⁰⁰⁰ = (1 + 0.1)¹⁰⁰⁰⁰

= $1^{10000} + 10000 C_{1} \times 1^{9999} {(0.1)}^{1}$

= 1 + 10000 x (0.1) + …. = 1001 +…

It is clear that the number (1.1)¹⁰⁰⁰⁰ is greater than 1000.

Hence, (1.1)¹⁰⁰⁰⁰ > 1000

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Binomial Theorem for Positive Integral Indices

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Q 10 Q 9 Q 11

Chapter 8: Binomial Theorem - Exercise 8.1 [Page 167]

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Chapter 8 Binomial Theorem
Exercise 8.1 | Q 10 | Page 167

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

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