sum of the finite geometric series ...
so ...
did the book leave off the or did you?
Hello everyone,
I'm not sure if this is the best category for my post, but i will try asking anyways. I've spent quite a bit of time trying to figure it out.
Basically, the problem involves calculating the output of a system to a given input and impulse response using convolution. That's probably the hardest part of the question, which I am able to do.
I get the output y[n] = summation(from k=0 to k=n) ((1/2)^k)*(1/3)^(n-k)
So i know that (1/3)^n can be brought outside the summation, and that
((1/2)^k)*(1/3)^(-k) = (3/2)^k, so the question can be simplified to
y[n]=((1/3)^n)*summation(k=0 to k=n) (3/2)^k
I know the formula for evaluating a sum from 0 to n, but for some reason i can't simplify it to the answer in the textbook. The answer i need is the following:
y[n]=2[((3/2)^(n+1))-1]
Any help is greatly appreciated.
The question can be seen here: http://www.site.uottawa.ca/~jpyao/co..._Fall_2004.pdf
Question #4