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5
questions
8
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1
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250
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Compute $\sum^{2024}_{k=1} \frac{2023-2022 \cos \left(\frac{\pi(2k-1)}{2024} \right)}{2021-2020 \cos \left(\frac{\pi(2k-1)}{2024} \right)}$
Question: Compute $$\sum^{2024}_{k=1} \frac{2023-2022 \cos \left(\frac{\pi(2k-1)}{2024} \right)}{2021-2020 \cos \left(\frac{\pi(2k-1)}{2024} \right)}$$
I began by rearranging the sum as follows:
$$\...
- 640
5
votes
2
answers
879
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If $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 40°=a$, then $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 175°=?$
I'm stuck in this question
If $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 40°=a$
$\sin 5°+\sin 10°+\sin15°+\cdots+\sin 175°=?$
I know that, (I asked before) $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 175°=\tan\...
user548054
2
votes
2
answers
842
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Find the $\frac mn$ if $T=\sin 5°+\sin10°+\sin 15°+\cdots+\sin175°=\tan \frac mn$
It's really embarrassing to be able to doesn't solve this simple-looking trigonometry question.
$$T=\sin(5^\circ) +\sin(10^\circ) + \sin(15^\circ) + \cdots +\sin(175^\circ) =\tan \frac mn$$
Find the ...
user548054
0
votes
3
answers
151
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An infinite sum in the product of sines
This is an undergrad or lower level question I need help with.
Evaluate $$\quad \sum_{n=1}^{\infty} \sin{\left(\frac{a}{3^n}\right)}\sin{\left(\frac{2a}{3^n}\right)}$$
where a is just some real ...
- 377
4
votes
2
answers
436
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Evaluating $\sum_{n=1}^{99}\sin(n)$ [duplicate]
I'm looking for a trick, or a quick way to evaluate the sum $\displaystyle{\sum_{n=1}^{99}\sin(n)}$. I was thinking of applying a sum to product formula, but that doesn't seem to help the situation. ...
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