| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Alternating series summation |
| Difficulty | Moderate -0.8 Both parts are straightforward pattern recognition exercises. Part (i) requires noticing that most terms cancel, leaving only 1 + 1/30. Part (ii) is a standard alternating series that pairs into (-1 + 2) + (-3 + 4) + ... yielding 50. These are routine manipulations with no conceptual depth or problem-solving required beyond recognizing the telescoping/pairing pattern. |
| Spec | 1.04g Sigma notation: for sums of series |
(i) Since most terms cancel, $(1 + 30^{-1})$ — M1; $= 1\frac{1}{30}$ — A1 **[2]**
(ii) $S = -1 + 2 - 3 + 4 - \ldots -99 + 100$ — M1; $= 50 \times 1 = 50$ — A1 **[2]**
**Total: [4]**8 Evaluate the following, giving your answers in exact form.\\
(i) $\sum _ { n = 1 } ^ { 30 } \frac { 1 } { n } - \sum _ { n = 2 } ^ { 29 } \frac { 1 } { n }$.\\
(ii) $\sum _ { n = 1 } ^ { 100 } n \times ( - 1 ) ^ { n }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q8 [4]}}