A-LevelFurther MathematicsSummation of series9231/12 · May/June 2021 · Q29 Marks
Use standard results from the List of formulae (MF19) to find ∑(1-r-r²) in terms of n, simplifying your answer.
- (a)Use standard results from the List of formulae (MF19) to find ∑(1-r-r²) in terms of n, simplifying your answer.[3]
- (b)Show that (1-r-r²)/((r²+2r+2)(r²+1)) = (r+1)/((r+1)²+1) - r/(r²+1) and hence use the method of differences to find ∑(1-r-r²)/((r²+2r+2)(r²+1))[5]
- (c)Deduce the value of ∑(1-r-r²)/((r²+2r+2)(r²+1))[1]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1A1] Substitutes correct formulae from MF19. Expanding brackets correctly.
- [A1] Simplifies by collecting terms.
- [M1 A1] Puts over a common denominator and expands, AG.
- [M1 A1] Shows at least three complete terms including first and last. Cancellation may be implicit.
- [A1] ISW
- [B1 FT] FT from their answer to part (b).
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →