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My book introduces difference equations as summations. They seem to be equations involving summations with different indices. I know what I've said is a little vague so here is an example question I have(not from the book I referred to).

Q. Find the general solution of the following difference equation.

[tex]y_{n + 1} - y_n = 2[/tex]

Answer: [tex]y_n = A\left( {\frac{1}{2}} \right)^n + 2[/tex]

Can someone explain to me what the equation actually means?. Any sort of explanation or references to useful websites would also be good. As I alluded to before I don't actually see the connection between difference equations and differential equations. Is it like when you have a real function f(x) and you the sequence f(n)? Any help would be appreciated.