2016 HCI P1 Q4
Timothy Gan
2016 HCI P1 Q4
Prove that $\frac{2n+1}{\sqrt{{{n}^{2}}+2n}+\sqrt{{{n}^{2}}-1}}=\sqrt{{{n}^{2}}+2n}-\sqrt{{{n}^{2}}-1}$.
[2]
Hence find $\sum\limits_{n=1}^{N}{\frac{2n+1}{\sqrt{{{n}^{2}}+2n}+\sqrt{{{n}^{2}}-1}}}$.
[3]
(a)
Deduce the value of $\sum\limits_{n=2}^{N}{\frac{2n-1}{\sqrt{{{n}^{2}}-2n}+\sqrt{{{n}^{2}}-1}}}$.
[3]
(b)
Show that $\sum\limits_{n=1}^{N}{\frac{2n+1}{2n-1}}>\sqrt{{{N}^{2}}+2N}$.
[1]
Suggested Video and Handwritten Solutions
Share with your friends!
- No charge
- Unsubscribe anytime
Continue reading
Introducing Our Sec 1 Assessment Book: From Concepts to Confidence
Welcome to Tim Gan Math Learning Centre, where we have been dedicated to nurturing mathematical excellence since our establishment in 2017. At our centre, we are committed to providing quality
Entangled in the Web: Managing Online Entertainment, Internet Addiction, and Academic Achievement in Math
In today’s digital age, the internet has seamlessly woven itself into the fabric of our daily lives, becoming an indispensable tool for communication, information, and, notably, entertainment. The allure of
Goal Setting and Progress Tracking for Math Students: A Comprehensive Guide
In the pursuit of academic success, setting and achieving goals play a pivotal role, particularly in disciplines like mathematics. Effective goal setting not only provides students with a roadmap for