Fourier transform of $ne^{-an}u[n]$ I need to find the Fourier transform of the following signal:

$$ne^{-an}u[n]$$

The answers start by using the rule of the basic signal:

$$a^nu[n] \rightarrow \frac{1}{1-ae^{-j\omega}} $$

and then uses the property of differentiation in the frequency domain. However I think there's something wrong with the way the rule is used. The answers assume that:

$$e^{-an}u[n] = a^nu[n] \rightarrow \frac{1}{1-ae^{-j\omega}} $$

Is there something wrong or am I missing something?



Here's the answer for reference:
You're right, the first Fourier transform correspondence in your reference is wrong. It should be

$$\mathcal{F}\{e^{-\alpha n}u[n]\}=\frac{1}{1-e^{-\alpha}e^{-j\omega}}\tag{1}$$

You just need to substitute $a=e^{-\alpha}$ and use the formulas you know.