1.4 Sequences and Series - The Binomial Theorem

Let $D (v)$ be a function representing the density of a gas relative to its volume $v$ , defined by

\left(2 - \frac{v}{8}\right)^{10}

Find the first 4 terms of the binomial expansion of $D (v)$ in ascending powers of $v$ , giving each coefficient as an integer.

[4]

A related physical quantity $Q\,$ is derived from the density function such that

\left(3 + \frac{2}{v}\right)^2 D(v)

Hence, find the constant term in the series expansion of $Q$ .

[3]

1.4 Sequences and Series - The Binomial Theorem Questions

Let $D (v)$ be a function representing the density of a gas relative to its volume $v$ , defined by

\left(2 - \frac{v}{8}\right)^{10}

Find the first 4 terms of the binomial expansion of $D (v)$ in ascending powers of $v$ , giving each coefficient as an integer.

[4]

A related physical quantity $Q\,$ is derived from the density function such that

\left(3 + \frac{2}{v}\right)^2 D(v)

Hence, find the constant term in the series expansion of $Q$ .

[3]