Hello,

I'm trying to show that y[n]=x[n]∗h[n] turns into Y(z)=X(z)H(z) in Z-domain by first applying convolution then by taking the inverse Z-transform of the Y(z), stating that it's the same sequence after all. However, in power series expansion an extra term appears which kills the equation. You can find the question below; I added it as an image.

I'd be grateful if you could help.
Thank you

 

There's a mistake on the 2nd line. I should've written x[m]

 

How about looking at the definitions of the Z transform and of convolution?