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    A series is defined by C and S below:

     C=2cos\theta + 4cos2\theta + 8cos3\theta + ... + 2^ncosn\theta

     S=2sin\theta + 4sin2\theta + 8sin3\theta + ... + 2^nsinn\theta

    The question is asking me to find expressions for both C and S, and I have no idea what to do. It is question 2)b)ii) on the link below:
    http://www.mei.org.uk/files/papers/fp208ja_lsgz.pdf

    Thanks
    Sora
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    (Original post by Sora)
    A series is defined by C and S below:

     C=2cos\theta + 4cos2\theta + 8cos3\theta + ... + 2^ncosn\theta

     S=2sin\theta + 4sin2\theta + 8sin3\theta + ... + 2^nsinn\theta

    The question is asking me to find expressions for both C and S, and I have no idea what to do. It is question 2)b)ii) on the link below:
    http://www.mei.org.uk/files/papers/fp208ja_lsgz.pdf

    Thanks
    Sora
    Consider summing  C+jS and grouping them together - see Exercise 3G for more detail
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    (Original post by Sora)
    A series is defined by C and S below:

     C=2cos\theta + 4cos2\theta + 8cos3\theta + ... + 2^ncosn\theta

     S=2sin\theta + 4sin2\theta + 8sin3\theta + ... + 2^nsinn\theta

    The question is asking me to find expressions for both C and S, and I have no idea what to do. It is question 2)b)ii) on the link below:
    http://www.mei.org.uk/files/papers/fp208ja_lsgz.pdf

    Thanks
    Sora
    Think about it this way cos\theta +isin\theta=e^{i\theta}
    Write the expression  C+iS in this way.
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    (Original post by Dualcore)
    Think about it this way cos\theta +isin\theta=e^{i\theta}
    Write the expression  C+iS in this way.
    Okay, I did this. What next?
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    (Original post by Sora)
    Okay, I did this. What next?
    Find the thing you have to times each term by to get to the next term, then use the geometric series formula for series.
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    (Original post by Dualcore)
    Find the thing you have to times each term by to get to the next term, then use the geometric series formula for series.
    I think I have that too, but I am still unsure of where to go
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    (Original post by Sora)
    I think I have that too, but I am still unsure of where to go
    Post what you have .
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    (Original post by Dualcore)
    Post what you have .
     C+jS = 2e^{j\theta} + 4e^{2j\theta} + ... + 2^ne^{nj\theta}

    From this we get the common ratio as:

     r = 2e^{j\theta}
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    (Original post by Sora)
     C+jS = 2e^{j\theta} + 4e^{2j\theta} + ... + 2^ne^{nj\theta}

    From this we get the common ratio as:

     r = 2e^{j\theta}
    What's the first term? What's the equation for summing geometric series from term 1 to term n?
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    (Original post by Sora)
     C+jS = 2e^{j\theta} + 4e^{2j\theta} + ... + 2^ne^{nj\theta}

    From this we get the common ratio as:

     r = 2e^{j\theta}
    Have you got an expression for the sum of all the terms using the formula?
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    (Original post by Sora)
    Okay, I did this. What next?
    You've written
    \displaystyle C+iS=\sum_1^n 2^n e^{in\theta}
    Then write down \displaystyle C-iS=\sum_1^n 2^n e^{-in\theta}
    Add them together and divide by 2. You will get C
    Subtract the 2nd from the 1st and divide by 2. You will get S
    Hint:
    \displaystyle \frac{e^{in\theta}+e^{-in\theta}}{2}=cosh(in\theta)= \cos (n\theta)
    \displaystyle \frac{e^{in\theta}-e^{-in\theta}}{2i}=\sin(n\theta)
 
 
 
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