Summation Question #2

This is a question from AJC/C2/MY/P1/10. Quite challenging. But once you get the hang of it, you should be capable of solving other variations.

Using the formula for $sin(A+B)$ , prove the $sin(3A)=3sinA-4sin^{3}A$ .

(i) Hence show that $\sum_{r=1}^{n} \frac{4}{3^r} sin^{3}(3^{r}\theta)=sin(3\theta)-\frac{1}{3^n} sin(3^{n+1}\theta)$

(ii) Deduce the sum of the series $\sum_{r=1}^{n} sin^{2}(3^{r}\theta)cos(3^{r}\theta)$

Ans: $\frac{1}{4} [cos(3\theta)-cos(3^{n+1}\theta)]$

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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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October 26th, 2017 02:22 PM

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Summation Question #2

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