Evaluate Sum - Couldn't Arrive at Answer

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The discussion focuses on a user struggling to solve a problem related to evaluating a sum, specifically arriving at the answer of 483/200. Participants emphasize the importance of breaking down the problem and showing previous work to facilitate assistance. There is a suggestion to simplify the task by adding up the nine terms involved. The thread is ultimately locked due to the original poster's lack of demonstrated effort in solving the problem. Overall, the conversation highlights the necessity of engaging with the problem to receive meaningful help.
martina1075
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Homework Statement
Good morning,

Can someone help me with solving this please?

Thank you in advance
Relevant Equations
As per picture
Couldn’t arrive to the answer
 

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You'll need to show us what you've done so far. Can you break the problem down?
 
PeroK said:
You'll need to show us what you've done so far. Can you break the problem down?
This is how far I went.
PeroK said:
You'll need to show us what you've done so far. Can you break the problem down?
I did not manage to break it down. The answer should be 483/200
 
martina1075 said:
This is how far I went.

I did not manage to break it down. The answer should be 483/200

We can't do your homework for you. If you really have no idea how to simplify the problem, then just add up. You've only nine terms to calculate and add together.

Doing that might give you some ideas of what you to do if ##k = 1## to ##100##, say.
 
Thread locked due to lack of effort shown by OP.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
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