4PM1/02 Jun 2020, Question 3: Binomial Series for Any Rational Power
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Expand (1 + px)^(−5) for p ≠ 0 as a series in ascending powers of x through the x⁴ term, simplifying each term, then use c₄ = 2c₃ to determine p.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Write the binomial expansion of (1 + px)^(−5) up to and including x⁴, giving every term in simplest form.
- 1(1 + px)^(−5) = 1 + (−5)(px) + (−5)(−6)(px)²/2! + (−5)(−6)(−7)(px)³/3! + (−5)(−6)(−7)(−8)(px)⁴/4!
- 2= 1 − 5px + 15p²x² − 35p³x³ + 70p⁴x⁴ + …
Answer1 − 5px + 15p²x² − 35p³x³ + 70p⁴x⁴
Part (b) · 2 marks
Given that the x⁴ coefficient equals twice the x³ coefficient, work out the value of p.
- 1c₄ = 70p⁴, c₃ = −35p³
- 270p⁴ = 2 × (−35p³) ⇒ 70p⁴ + 70p³ = 0
- 370p³(p + 1) = 0, p ≠ 0 ⇒ p = −1
Answerp = −1
Stuck on a step? Read the free lesson: Binomial Series for Any Rational Power
Practise more binomial series for any rational power questions
Real 4PM1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on binomial series for any rational power
Also searched as: 4PM1 2 June 2020 · 4PM1/02 · 4pm1 jun20 2 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.