I want to find the coefficient $b_k$ of Fourier Series but I am stuck. The formula is:

$$\frac{1}{10}\sum_{n=0}^{9} e^{-jk\omega_0n}$$

In order to solve this I am using the following formula:

$$\sum_{n_1}^{n_2} \alpha^{n} = \frac{\alpha^{n_1}-\alpha^{n_2+1}}{1-\alpha}$$ I have tried everything but I am unable to reach the answer. The answer is: $$\frac{1}{10}(1-e^{-j\omega_08k})$$

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closed as off-topic by Stanley Pawlukiewicz, lennon310, Dilip Sarwate, MBaz, Matt L. Nov 9 at 10:12

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  • hint. exp(j theta)=exp(j theta/2)exp(jtheta/2). – Stanley Pawlukiewicz Nov 8 at 16:22
  • @StanleyPawlukiewicz please solve and post it. I'm stuck at it for hours. – Ahmad Qayyum Nov 8 at 16:25
  • 4
    because i’m not your mother. you got 2 reasonable hints. take a break. some people do well after a run. kill some alien invaders. this is not a hard – Stanley Pawlukiewicz Nov 8 at 17:08
  • 3
    @AhmadQayyum because we're not a "do your homework for you even if you don't understand it" website. We're a "helping you do your homework yourself" community. We will explain what you need to do. We will never do it for you. If you look for someone to do your homework for you, please go somewhere else. If you want to learn how to do it yourself, do it yourself, and get confident it's right: this is the place to be! Our answers are typically pretty in-depth, as this is really about exchanging knowledge, not solutions to assignments. – Marcus Müller Nov 8 at 17:16
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    I'm voting to close this question as off-topic because of no reasonable attempt at exercise – Stanley Pawlukiewicz Nov 8 at 17:30

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