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# Use binomial theorem to evaluate the following upto four places of decimal (1.02)–5 - Mathematics and Statistics

Sum

Use binomial theorem to evaluate the following upto four places of decimal

(1.02)–5

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#### Solution

(1.02)–5 = (1 + 0.02)–5

= 1 + (-5)(0.02) + ((-5)(-5 - 1))/(2!)(0.02)^2 + ((-5)(-5 - 1)(-5 - 2))/(3!)(0.02)^3 + ...

= 1 - 0.1 + (-5)(-6)(1/2)(0.0004) + (-5)(-6)(-7)(1/6)(0.000008) + ...

= 1 – 0.1 + 0.006 – 0.00028 + ...

= 1.006 – 0.10028

= 0.9057, upto 4 places of decimals.

Concept: Binomial Theorem for Negative Index Or Fraction
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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 4.4 | Q 4. (iv) | Page 82
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