1.6: A binomial expansion with related coefficients

4PM1/2/November/2020 — Question 3 · 5 marks

(a) Expand
(1+px)−5,p≠0,(1+px)^{-5}, \qquad p\neq0,
in ascending powers of x\displaystyle x, up to and including the term in x4\displaystyle x^4. Give each term in its simplest form.
(3)
The coefficient of xr\displaystyle x^r in the expansion is cr\displaystyle c_r. Given that
c4=2c3,c_4=2c_3,
(b) find the value of p\displaystyle p.
(2)