Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    Precalculus or calculus text.

  5. Mar 8, 2008 #4


    User Avatar

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook