2016 NJC P2 Q1
2016 NJC P2 Q1
5 marks
Prelims
- Kenny took a loan of \(\$9600\) from a friend, and arranged to pay his loan fully in a period of exactly \(48\) months. To fulfil this arrangement, he paid \(\$a\) on the last day of the first month, and on the last day of each subsequent month, he paid \(\$d\) more than in the previous month. However, due to financial difficulties, Kenny stopped his payments after his \({{40}^{\mathrm{th}}}\) payment, and as a result he still had exactly \(\$2400\) left unpaid.In which month did Kenny first pay at least \(\$130\) on the last day of that month?[5]
- Explain why the series \(1+{{\mathrm{e}}^{-2x}}+{{\mathrm{e}}^{-4x}}+...\) converges for any positive real number \(x\), and express the sum to infinity in terms of \(x\).[2]
- Given that \(x=10\), find the least value of \(n\) such that \(S-{{S}_{n}}<S\left( {{10}^{-100}} \right)\), where \(S\) and \({{S}_{n}}\) represent the sum to infinity and the sum of the first \(n\) terms of the series respectively.[3]
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(a) 11th month; (b)(i) \(\frac1{1-e^{-2x}}\); (b)(ii) \(n=12\)
Need help? Join our JC Math tuition classes.
Learn more