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Signals class math problem

  1. Mar 7, 2008 #1
    hi everyone,

    i had a class where my teacher was talking about this but i dont know where this comes from, if anyone knows could you please give hint on the type of material this is. Like what type of mathbook i should be looking for.

    the problem was:

    Demonstrate the following expression:

    [tex]\[\displaystyle\sum_{n=0}^{N-1} \alpha^n = \left\{
    \begin{array}{l l}
    N & \quad \mbox{, $\alpha$ = 1}\\
    \frac{1-\alpha^N}{1-\alpha} & \quad \mbox{, for any complex, $\alpha$ $\neq$ 1}\\ \end{array} \right. \][/tex]

    thankyou very much for any help.
  2. jcsd
  3. Mar 7, 2008 #2
    Well, the case where [itex]\alpha=1[/itex] should be easy enough. To demonstrate the second case, simply multiply the summation by the fraction [itex]\frac{1-\alpha}{1-\alpha}[/itex]. This will give you the denominator you need, and some subsequent simplifications to the numerator give you the final answer.
  4. Mar 7, 2008 #3


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    Science Advisor

    Precalculus or calculus text.

  5. Mar 8, 2008 #4


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    in other words, ask yourself why the following is true:

    [tex](1-\alpha)\sum_{n=0}^{N-1} \alpha^n = \sum_{n=0}^{N-1} \alpha^n - \alpha\sum_{n=0}^{N-1} \alpha^n = 1 - \alpha^N [/tex]

    if you can figger out why that is true, you've solved your problem.
  6. Mar 9, 2008 #5
    thanks for the help i found it in a calculus book. it´s mathematical induction.

    i can use the homogeneous property...and thus get the anwser

    anyway thankyou all for helping out.
    Last edited: Mar 9, 2008
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