## Question 10:

**Part (i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| | M1 | Use correct denominator |
| | A1 **2** | Obtain given answer correctly |

**Part (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| | M1 | Express terms as differences using (i) |
| | M1 | Do this for at least 3 terms |
| $\frac{1}{2} - \frac{1}{n+1} + \frac{1}{n+2}$ | A1 | First 3 terms all correct |
| | A1 | Last 2 terms all correct |
| | M1 | Show relevant cancelling |
| | A1 **6** | Obtain correct answer a.e.f. |

**Part (iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{2}$ | B1ft | $S_\infty$ stated or start at $n+1$ as in (ii) |
| $\frac{1}{n+1} - \frac{1}{n+2}$ | M1 | $S_\infty$ minus their (ii) or show correct cancelling |
| $\frac{1}{(n+1)(n+2)}$ | A1 **3** | Obtain given answer correctly |