Series (FP1) — Edexcel International A-Level Further Mathematics
Edexcel International A-Level Further Mathematics · IAL Further Maths FP1 · 15 min read
1. Linearity of Summation Rules★★☆☆☆⏱ 4 min
This rule is the foundation of all FP1 series problems. It lets you break down complex composite summations into separate, simpler terms that match the standard summation results you can use directly.
Exam tip: Always split constants out first, and remember that a term with no r (e.g. -5) is summed n times, not once.
2. Standard Summation Results★★★☆☆⏱ 5 min
These three results are the only standard summations you will need for FP1 series questions. Any polynomial term in r can be expanded and split into combinations of these three sums using linearity rules.
Exam tip: Always double-check your substitution of n into the formulae, especially for the $\sum r^2$ result which has the (2n+1) factor that is easy to mix up.
3. Simplifying to Fully Factorised Closed Form★★★★☆⏱ 6 min
After substituting the standard results into your split summation, you will be left with a polynomial expression in n. You must simplify this to a fully factorised form, as required by the exam specification. Factorising makes it easier to evaluate for specific values of n and is often explicitly asked for in questions.
Common Pitfalls
Why: The constant term is included for every one of the n values of r, so it is added n times, not once.
Why: The method of differences is not part of the FP1 specification, and you will not receive marks for using it even if you get the correct answer.
Why: This will result in an incorrect final answer, even if your algebraic manipulation is correct.
Why: Exam questions often explicitly require a fully factorised form, so you will lose marks for not factorising even if your expanded expression is correct.
Why: Algebraic errors at the first step of the problem will invalidate all subsequent working.