Simplify first three terms in the expansion of the following (1 + 2x)–4 - Mathematics and Statistics

Simplify first three terms in the expansion of the following

(1 + 2x)^–4

Sum

(1 + 2x)^–4

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

= `1 - 8x + ((-4)(-5))/2 (4x^2) + ...`

= 1 – 8x + 40x² + ......

shaalaa.com

Binomial Theorem for Negative Index Or Fraction

Is there an error in this question or solution?

Chapter 4: Methods of Induction and Binomial Theorem - Exercise 4.4 [Page 82]

Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 3. (i) | Page 82

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

`(1 - x)^(1/3)`

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

`(1 + x)^(-1/5)`

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

(1 + x²)^–1

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a − b)⁻³

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a + b)⁻⁴

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" + "b")^(1/4)`

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" - "b")^(-1/4)`

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" + "b")^(-1/3)`

Simplify first three terms in the expansion of the following

`(1 + 3x)^(-1/2)`

Simplify first three terms in the expansion of the following

`(2 - 3x)^(1/3)`

Simplify first three terms in the expansion of the following

`(5 + 4x)^(-1/2)`

Simplify first three terms in the expansion of the following

`(5 - 3x)^(-1/3)`