Summation Question #1

This is a modified summation question taken from HCI. I think it forces the students to think out of the box, and we all know how scary trigonometry and summation is together.

Given $\sum_{r=1}^{n}cos[(2r-1){\theta}] = \frac{sin(2n\theta)}{2sin\theta}$ , show that

$sin{\theta}+3sin{3\theta}+5sin{5\theta}+...+99sin{99\theta} = \frac{cos{\theta}sin{100\theta}-100sin{\theta}cos{100\theta}}{2sin^{2}\theta}$

Hint: try writing out what you’re given and contrast it with what you are attempting to show. 🙂

Question Summation

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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