State the range of values of x for which the binomial expansion of $$ \sqrt{1 - \frac{x}{4}} $$ is valid - AQA - A-Level Maths Pure - Question 1 - 2022 - Paper 3

For the binomial expansion to be valid, the expression inside the square root must be non-negative. This requires:

$$1 - \frac{x}{4} \geq 0$$

Solving this inequality:

$$1 \geq \frac{x}{4}$$

or equivalently,

$$\frac{x}{4} \leq 1$$

Thus, multiplying both sides by 4, we get:

$$x \leq 4$$

Also, since we are dealing with absolute values, we have:

$$|x| < 4$$

This is the valid range of values for x for which the binomial expansion is valid.