likeneverbefore
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- May 15, 2015
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- HSC
- 2016
Hi everyone i was wondering whether you could help me with these questions and provide written worked solutions if possible!!! Theyre too hard ahah THANKS!
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Need help with these qs (sourced from ekman) (1 Viewer)
- Thread starter likeneverbefore
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Hi everyone i was wondering whether you could help me with these questions and provide written worked solutions if possible!!! Theyre too hard ahah THANKS!
likeneverbefore
New Member
- Joined
- May 15, 2015
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- 9
- Gender
- Male
- HSC
- 2016
Thanks!!! Awesome explanations i understand now!
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likeneverbefore
New Member
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- May 15, 2015
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- Gender
- Male
- HSC
- 2016
Hi integrand thanks for your answer!!! i was just wondering how you would know to start with what S is?^{k} \frac{\sin ((2k+1)\theta)}{9^k}$. This is the imaginary part of the geometric series $\widetilde{S} = \sum_{k=0}^{\infty} \left(-\frac{1}{9}\right)^{k} \mathrm{cis}\left((2k+1)\theta\right)$. This has common ratio $-\frac{1}{9}\mathrm{cis}\left(2\theta\right)$, which has modulus less than $1$, so that the series is convergent. Use the GP sum formula to get this sum, then find its imaginary part to get the answer.$)
I simply wrote S for the given sum so that we have a variable assigned to it if we need to refer to it (so it's more convenient to have to keep referring to it as "the sum" and so we can write equations involving it etc.).