How to append multiple items in one line in Python

No.

First off, append is a function, so you can't write append[i+1:i+4] because you're trying to get a slice of a thing that isn't a sequence. (You can't get an element of it, either: append[i+1] is wrong for the same reason.) When you call a function, the argument goes in parentheses, i.e. the round ones: ().

Second, what you're trying to do is "take a sequence, and put every element in it at the end of this other sequence, in the original order". That's spelled extend. append is "take this thing, and put it at the end of the list, as a single item, even if it's also a list". (Recall that a list is a kind of sequence.)

But then, you need to be aware that i+1:i+4 is a special construct that appears only inside square brackets (to get a slice from a sequence) and braces (to create a dict object). You cannot pass it to a function. So you can't extend with that. You need to make a sequence of those values, and the natural way to do this is with the range function.

You could also:

newlist += mylist[i:i+22]

No. The method for appending an entire sequence is list.extend().

>>> L = [1, 2]
>>> L.extend((3, 4, 5))
>>> L
[1, 2, 3, 4, 5]