These Ten-Year-Series (TYS) worked solutions with video explanations for 2009 A Level H2 Mathematics Paper 1 Question 3 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2009 A Level H2 Math Paper 1 Question 3
(i)
Show that $\frac{1}{n-1}-\frac{2}{n}+\frac{1}{n+1}=\frac{A}{{{n}^{3}}-n}$, where $A$ is a constant to be found.
[2]
(i) Show that $\frac{1}{n-1}-\frac{2}{n}+\frac{1}{n+1}=\frac{A}{{{n}^{3}}-n}$, where $A$ is a constant to be found.
[2]
(ii)
Hence find $\sum\limits_{r=2}^{n}{\frac{1}{{{r}^{3}}-r}}$, (There is no need to express your answer as a single algebraic fraction.)
[3]
(ii) Hence find $\sum\limits_{r=2}^{n}{\frac{1}{{{r}^{3}}-r}}$, (There is no need to express your answer as a single algebraic fraction.)
[3]
(iii)
Give a reason why the series $\sum\limits_{r=2}^{\infty }{\frac{1}{{{r}^{3}}-r}}$ converges, and write down its value.
[2]
(iii) Give a reason why the series $\sum\limits_{r=2}^{\infty }{\frac{1}{{{r}^{3}}-r}}$ converges, and write down its value.
[2]
Suggested Video Solutions
Suggested Handwritten Solutions
Share with your friends!
Continue reading
Maximizing June Holidays: Is Joining a Crash Course Necessary?
As June holidays approach, students find themselves at a crucial juncture in their academic journey. With the semester winding down and exams looming on the horizon, the pressure to excel
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