| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | February |
| Marks | 6 |
| Topic | Geometric Sequences and Series |
| Type | Find N for S_∞ - S_N condition |
| Difficulty | Standard +0.3 This is a straightforward geometric series question requiring (a) simple term generation and (b) finding n where S_n > 0.998×S_∞. Part (a) is trivial arithmetic. Part (b) requires knowing S_∞ = a/(1-r) = 40, then solving 40(1-0.5^(n+1)) > 39.92, which reduces to a simple logarithm calculation. Standard textbook exercise with clear method and no novel insight required, making it slightly easier than average. |
| Spec | 1.04j Sum to infinity: convergent geometric series |r|<1 |
3 In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alph*)]
\item Write down the first 5 terms of the geometric series
$$\sum _ { r = 0 } ^ { n } 20 \times 0.5 ^ { r }$$
\item Find the smallest value of $n$ for which the series
$$\sum _ { r = 0 } ^ { n } 20 \times 0.5 ^ { r }$$
is greater than $99.8 \%$ of its sum to infinity.\\[0pt]
[5]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q3 [6]}}