2023 NYJC MYE P1
The series $a+ar-a{{r}^{2}}-a{{r}^{3}}+a{{r}^{4}}+a{{r}^{5}}-a{{r}^{6}}-a{{r}^{7}}+$…, where $a>0$, has its $k$th term, ${{T}_{k}}$, defined by ${{T}_{k}}=\left\{ \begin{matrix}
a{{r}^{k-1}}, \\
-a{{r}^{k-1}}, \\
\end{matrix} \right.$ $\begin{matrix}
\text{if}\,k=4p-3\,\,\text{or}\,\,4p-2 \\
\text{if}\,k=4p-1\,\,\text{or}\,\,4p\,\,\,\,\,\,\, \\
\end{matrix}$, for $p\in {{\mathbb{Z}}^{+}}$,
(a)
By rewriting the series as the sum of two geometric series, or otherwise, prove that the sum to $4n$ terms of the series is $\frac{a(1+r)(1-{{r}^{4n}})}{1+{{r}^{2}}}$.
[3]
(b)
State the set of values of $r$ for which the series has a sum to infinity.
[1]
(c)
Given that $r=-0.9$, find the least value of $n$ for the sum of $4n$ terms to be greater than $99\%$ of the sum to infinity.
[3]
Suggested Video Solutions
Share with your friends!
Continue reading
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration
Panic No More: What To Do The Day Before An Exam?
As you approach the final hours before your exam, remember that a balanced approach is key. A light review can keep the information fresh in your mind, while preparing your