AS June 2019 Paper 1 Q1
1 In this question you must show detailed reasoning.
Find \(\displaystyle\sum_{r=1}^{100}\left(\frac{1}{r} - \frac{1}{r + 2}\right)\), giving your answer correct to 4 decimal places. [3]
| Scheme | Marks | AO |
|---|---|---|
| DR \(\displaystyle\sum_{r=1}^{100}\left(\frac{1}{r} - \frac{1}{r + 2}\right) = 1 - \frac{1}{3} + \frac{1}{2} - \frac{1}{4} + \frac{1}{3} - \frac{1}{5} + \ldots + \frac{1}{100} - \frac{1}{102}\) | M1 | 2.5 |
| \(= 1 + \dfrac{1}{2} - \dfrac{1}{101} - \dfrac{1}{102}\) | A1 | 2.2a |
| \(= 1.4803\) (4 d.p.) | A1cao | 1.1 |
| [3] |
Notes
M1: must see at least one cancellation
A1: or \(1 + \dfrac{1}{2} - \dfrac{1}{n + 1} - \dfrac{1}{n + 2}\)
A1cao: must be to 4 DP