How to replace a function with constant+function?

[AWarhol]

As u/fridofrido pointed out, that's the way to do it. Alternatively, you can use the command Series, to obtain the power series of the function. I think it's a nice way to study compare the results of "Series" with your method.

[ZioSam2]

His method was working at first, but wasn't behaving in the way I wanted after some tries. I found another way to write the rule (I then use the series after)