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Using binomial theorem, find the value of (0.9)4 - Mathematics and Statistics

Sum

Using binomial theorem, find the value of (0.9)4 

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Solution

(0.9)4 = (1 – 0.1)4

= 4C0(1)44C1(1)3(0.1) + 4C2(1)2(0.1)24C3(1)(0.1)3 + 4C4(0.1)4 

Now, 4C0 = 1 = 4C4

4C1 = 4 = 4C3

4C2 = `(4 xx 3)/(1 xx 2)` = 6

∴ (0.9)4 = 1 × 1 – 4 × 1 × 0.1 + 6 × 1 × 0.01 – 4 × 1 × 0.001 + 1 × 0.0001

= 1 – 0.4 + 0.06 – 0.004 + 0.0001

= 1.0601 – 0.404

= 0.6561

Concept: Binomial Theorem for Positive Integral Index
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.2 | Q 6. (ii) | Page 77
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