1.4.1 Sequences and Series - The Binomial Theorem

The first three terms, in ascending powers of $x$ , of the binomial expansion of $5x)^{\frac{1}{2}}$ are given by

5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2

where $a$ is a constant.

State the range of values of $x$ for which this expansion is valid.

Choose from the options below:

\frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1

[2]

Find the value of $a$ .

Choose from the options below:

\quad 4 \quad 8 \quad 16

[2]

1.4.1 Sequences and Series - The Binomial Theorem Questions

The first three terms, in ascending powers of $x$ , of the binomial expansion of $5x)^{\frac{1}{2}}$ are given by

5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2

where $a$ is a constant.

State the range of values of $x$ for which this expansion is valid.

Choose from the options below:

\frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1

[2]

Find the value of $a$ .

Choose from the options below:

\quad 4 \quad 8 \quad 16

[2]