Question (1) (a to g) "State the limits of the following sequences, or state that the limit does not exist."

Five of these sequences work something like this (in that they can be represented by an equation):

(b) 5, 4 + 1/2, 4 + 1/3, 4 + 1/4, 4 + 1/5, . . . ,4 + 1/n, . . .

. . . which means I can write

lim x ->(infinity) 4 + 1/n

= 4 + (0)

= 4

However, two of these sequences cannot be expressed with an equation. They are:

(e) 1, 0, 1/2, 0, 1/3, 0, 1/4, 0, . . .

and

(g) 1, 1/2, 1, 1/3, 1, 1/4, 1, 1/5, . . .

I can see that (e) approaches 0, and that (g) does not exist, but how can I show this in writing?

Any help is greatly appreciated.