# Using binomial theorem, find the value of (1.1)5 - Mathematics and Statistics

Sum

Using binomial theorem, find the value of (1.1)5

#### Solution

(1.1)5 = (1+ 0.1)5

= 5C0(1)5 + 5C1(1)4 (0.1) + 5C2(1)3 (0.1)2 + 5C3(1)2 (0.1)3 + 5C4(1) (0.1)4 + 5C5(0.1)5

Now, 5C0 = 1 = 5C5

5C1 = 5 = 5C4

5C2 = (5 xx 4)/(1 xx 2) = 10 = 5C3

∴ (1.1)5 = 1 + 5 × 1 × 0.1 + 10 × 1 × 0.01 + 10 × 1 × 0.001 + 5 × 1 × 0.0001 + 0.00001

= 1 + 0.5 + 0.1 + 0.01 + 0.0005 + 0.00001

= 1.61051

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 5. (ii) | Page 77