Maharashtra State BoardHSC Science (General) 11th
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State, by writing first four terms, the expansion of the following, where |x| < 1 (1 + x2)–1 - Mathematics and Statistics

Sum

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x2)–1

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Solution

(1 + x2)–1

= `1 + (-1)x^2 + ((-1)(-1 - 1))/(2!)(x^2)^2 + ((-1)(-1 -1)(-1 - 2))/(3!) (x^2)^3 + ...`

= `1 - x^2 + ((-1)(-2))/2 x^4 + ((-1)(-2)(-3))/6 x^6 + ...`

= 1 – x2 + x4 – x6 + ...

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 1. (v) | Page 82
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