1.3 Sequences and series

A signal processor's response function $R (x)$ is defined by the expansion of $R(x) = (2x - 5)^8$ .

Show that the first three terms, in descending powers of $x$ , of this expansion are given by

256x^8 + ax^7 + bx^6

where $a$ and $b$ are integers to be found.

[3]

Find the constant term in the expansion of

\left(2x - \frac{5}{x}\right)^8

[3]

1.3 Sequences and series Questions

A signal processor's response function $R (x)$ is defined by the expansion of $R(x) = (2x - 5)^8$ .

Show that the first three terms, in descending powers of $x$ , of this expansion are given by

256x^8 + ax^7 + bx^6

where $a$ and $b$ are integers to be found.

[3]

Find the constant term in the expansion of

\left(2x - \frac{5}{x}\right)^8

[3]