2.10: Binomial theorem and expansion applications

0606/23/M/J/16 — Question 8 · 7 marks · Binomial

(a)(i)

Use the Binomial Theorem to expand

(a + b)^{4}

, giving each term in its simplest form.

[2]

(a)(ii)

Hence find the term independent of

x

in the expansion of

\left(2x + \tfrac{1}{5x}\right)^{4}

[2]

(b)

The coefficient of

x^{3}

in the expansion of

\left(1 + \tfrac{x}{2}\right)^{n}

equals

\tfrac{5n}{12}

. Find the value of the positive integer

n

[3]