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I have a question to do with doing a Z-Transform on a Dirac function for signal processing. So if we have $x(n)=\delta (n)+\delta (n-1)$the transform should look like $X(z)=\sum (\delta (n)+\delta (n-1))z^{-n}$ with the sum going to infinity.

I would've thought solving this it would give me the answer $X(z)=1+z^{-1}$However, the answer I have been given is $X(z)=1+z^{-n}$. I just don't understand why the $n$ is still in the equation after it has been summed.

Here is the Z-Transform formula and x(n)

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