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Further algebra and series formulae
The 5 results the further algebra and series notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 5, the formulae booklet prints 3 and 2 are yours to memorise.
Further Maths · 3 lessons with formulae.
A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.
α + β + γ = -ba, αβ + αγ + βγ = ca, αβγ = -daα + β + γ = -(b/a), αβ + αγ + βγ = (c/a), αβγ = -d/a NOT IN THE BOOKLET: LEARN ITConditionsα, β, γ the roots of ax³ + bx² + cx + d = 0 with a ≠ 0, counted with multiplicity. Σ r = n(n+1)2Σ r = (n(n + 1))/2 NOT IN THE BOOKLET: LEARN ITConditionsSummed from r = 1 to n, with n a positive integer. Σ r2 = n(n+1)(2n+1)6, Σ r3 = n2(n+1)24Σ r^2 = ((n(n + 1)(2n + 1))/6), Σ r^3 = (n^2(n + 1)^2)/4 IN THE FORMULAE BOOKLETConditionsSummed from r = 1 to n, with n a positive integer. f(x) = f(0) + f'(0)x + f''(0)2!x2 + …f(x) = f(0) + f′(0)x + (f′′(0)/2!)x^2 + … IN THE FORMULAE BOOKLETConditionsf and all its derivatives must exist at 0, and the series must converge to f(x) over the range used. ln(1 + x) = x - x22 + x33 - x44 + … (-1 < x ≤ 1)ln(1 + x) = x - x^2/2 + x^3/3 - x^4/4 + … (-1 < x ≤ 1) IN THE FORMULAE BOOKLETConditions−1 < x ≤ 1, as printed. Outside that the series diverges. Every formula in the library is indexed by unit on the equation index, and the further algebra and series notes are where these results are derived and used. The 2 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.
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