General Binomial Theorem/Examples

Examples of Use of General Binomial Theorem

Example: $\paren {1 - x}^{-3}$

$\paren {1 - x}^{-3} = 1 + 3 x + 6 x^2 + 10 x^3 + \cdots$

Example: $\paren {1 + 2 x}^{-\frac 3 2}$

$\paren {1 + 2 x}^{-\frac 3 2} = 1 - 3 x + \dfrac {15} 2 x^2 - \dfrac {35} 2 x^3 + \cdots$

Example: $\paren {1 + 5 x}^{\frac 1 5}$

$\paren {1 + 5 x}^{\frac 1 5} = 1 + x - 2 x^2 + 6 x^3 + \cdots$

Example: $\paren {1 - 4 x}^{\frac 1 2}$

$\paren {1 - 4 x}^{\frac 1 2} = 1 - 2 x - 2 x^2 + 4 x^3 + \cdots$