Define and .

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Define

P(x)=\left(x+\dfrac{1}{x}\right)^{10}

and

Q(x)=\left(x-\dfrac{1}{x}\right)^{10}

. (i) Show that each of

P(x)

and

Q(x)

contains a term that is independent of

x

. (ii) Find individually the independent terms in

P(x)

and

Q(x)

. (iii) Hence compute the value of

P(1)+Q(1)