Maharashtra State BoardHSC Science (General) 11th
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Answer the following: Using binomial theorem, find the value of 9953 upto four places of decimals - Mathematics and Statistics

Sum

Answer the following:

Using binomial theorem, find the value of `root(3)(995)` upto four places of decimals

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Solution

`root(3)(995) = (995)^(1/3)`

= `(100 - 5)^(1/3)`

= `[100 (1 - 5/1000)]^(1/3)`

= `10(1 - 5/1000)^(1/3)`

= `10[1 - 1/3(5/1000) + (1/3(1/3 - 1))/(2!) (5/1000)^2 - ...]`

= `10[1 - 1/600 + 1/3((-2)/3)(1/2)(1/200)^2 - ...]`

= 10[1 – 0.00167 + ...]

= 10(0.99833)

= 9.9833

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
Miscellaneous Exercise 4 | Q II. (21) | Page 86
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