# Signals class math problem

1. Mar 7, 2008

### N468989

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:

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

thankyou very much for any help.

2. Mar 7, 2008

Well, the case where $\alpha=1$ should be easy enough. To demonstrate the second case, simply multiply the summation by the fraction $\frac{1-\alpha}{1-\alpha}$. This will give you the denominator you need, and some subsequent simplifications to the numerator give you the final answer.

3. Mar 7, 2008

### stewartcs

Precalculus or calculus text.

CS

4. Mar 8, 2008

### rbj

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

$$(1-\alpha)\sum_{n=0}^{N-1} \alpha^n = \sum_{n=0}^{N-1} \alpha^n - \alpha\sum_{n=0}^{N-1} \alpha^n = 1 - \alpha^N$$

if you can figger out why that is true, you've solved your problem.

5. Mar 9, 2008

### N468989

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