I'm working in a signals class for continuous signals, and we have this problem shown above. I have tried using this function `f_1 X f_2 = F_1 * F_2`, where I'm assuming this means multiplication of two functions is equal to the convolution of their fourier transforms. I'm using `f_1 = 0.5^n` and `f_2 = u(n)`.

So I can calculate the fourier transorm of `u(n)` fine. It is `(pi)(delta)(w) + 1/(jw))`. However, I cannot for the life of me figure out `0.5^n`. I tried to put it into the fourier transform integral `integral of (0.5^t)/(e^(jwt))dt` from `negative infinity to infinity`, but I end up with 0.5t/(e^(jw)), and when evaluated from `negative infinity to infinity`, I end up with `infinity` as my answer, unless of course the integration is wrong.

Therefore, either the answer is `infinity * (pi)(delta)(w) + 1/(jw)`, which when convoluted would equal just the second function..? OR am I going about this problem completely wrong?