Mathematics AA: SEQUENCES - SERIES Topical Past Paper Questions

[Maximum mark:29] The following question uses Maclaurin series to investigate approximations of mathematical constants and the accuracies of such approximations. (a) Given $ |x| [2] (b) Hence, use integration to show that the Maclaurin series of $ \arctan x $ may be expressed as…

[Maximum mark: 7] The sum of the first $n$ terms of a geometric sequence is given by $S_{n}=\sum_{r=0}^{n-1}5\left(\log_{2}c\right)^{r}$. (a) Given that $S_{n}$ converges, find the range of possible values of $c$. [3] (b) In the case where $c=1.5$, find the least value of $n$ suc…

[Maxn.. Give your answers to parts (a)(ii), (c)(i) and (d) correct to two decimal places. Daniela and Sorin have each recently received some money. Daniela won a cash prize and Sorin received an inheritance. Daniela had two options to choose from to receive her winnings. In both…