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Math Help - need help with series and differentiation. answers are provided. but don't understand

  1. #1
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    need help with series and differentiation. answers are provided. but don't understand

    in the first image, I don't understand how i'm supposed to get those two terms. and for the second image, i don't understand how I'm supposed to get this equation.


    thanks in advance
    Attached Thumbnails Attached Thumbnails need help with series and differentiation. answers are provided. but don't understand-maths1.jpg   need help with series and differentiation. answers are provided. but don't understand-maths2.jpg  
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  2. #2
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    Opalg's Avatar
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    In the first image, the term \frac{\sin\theta}r\frac{\cos\theta}r\partial_\thet  a seems to have been added and then subtracted, in one line of the calculation, for no reason whatever. Those terms don't appear in either the previous line or the following line of the calculation, and the whole thing would be improved if you just wipe them out.

    In the second image, if S_N(\theta) = \sum_{n=-N}^Ne^{in\theta} then e^{i\theta}S_N(\theta) = \sum_{n=-N}^Ne^{i(n+1)\theta}. This is the same as the sum defining S_N(\theta), except that the first term has been dropped, and one term has been added at the end.
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