A-LevelFurther MathematicsSummation of series9231/12 · May/June 2025 · Q18 Marks
Use standard results from the list of formulae (MF19) to show that n Σ(2-3r)(5-3r) = an³ +bn² +cn, r=1 where a, b and c are integers to be determined.
- (a)Use standard results from the list of formulae (MF19) to show that n Σ(2-3r)(5-3r) = an³ +bn² +cn, r=1 where a, b and c are integers to be determined.[3]
- (b)Use the method of differences to find n 1 Σ ----------- r=1 (2-3r)(5-3r) in terms of n.[4]
- (c)Deduce the value of ∞ 1 Σ ----------- r=1 (2-3r)(5-3r)[1]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] (2-3r)(5-3r) = 9r² - 21r + 10
- [M1] Substitutes formulae for Σr² and Σr.
- [A1] = 3n³ - 6n² + n
- [B1] Finds partial fractions.
- [M1 A1] Writes at least three terms, including first and last, to demonstrate cancelation.
- [A1] = -1/6 + 1/(3(2-3n))
- [B1] Allow FT from (b) if of similar form. (= -1/6)
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