A-LevelFurther MathematicsSummation of series9231/12 · May/June 2023 · Q37 Marks
Use the method of differences to find ∑(from r=1 to n) (1 / ((kr+1)(kr-k+1))) in terms of n and k, where k is a positive constant.
- (a)Use the method of differences to find ∑(from r=1 to n) (1 / ((kr+1)(kr-k+1))) in terms of n and k, where k is a positive constant.[4]
- (b)Deduce the value of ∑(from r=1 to ∞) (1 / ((kr+1)(kr-k+1)))[1]
- (c)Find also ∑(from r=n to 2n) (1 / ((kr+1)(kr-k+1))) in terms of n and k.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- M1 A1 Finds partial fractions.
- M1 Writes at least three complete terms, including last.
- A1 OE e.g. n/(kn+1)
- B1 1/k
- M1 Or applies the method of differences again.
- A1 OE e.g. 1/k * (1/(kn+1) - 1/(k(2n)+1))
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