A possible formula of sequence 0,1,0, - 1,0,1,0, - 1... Is

A possible formula of sequence 0,1,0, - 1,0,1,0, - 1... Is

Is sin (n π / 2 - π / 2)

Does sequence 1 / N have a limit
The sequence an = 1 / N is divergent, but isn't its limit 0

The limit of sequence an = 1 / N is 0, so it is convergent, but the series an = 1 / N is divergent
That is 1 / 1 + 1 / 2 + 1 / 3 +... + 1 / N = + ∞, (n - > + ∞)

Is there a limit for constant value sequence
It is said that sequence 1, - 1,1, - 1,1, - 1,1, - 1,1, - 1,1 It's divergent
What about the constant sequence?

The limit is the constant
1,1,1,1,1,1,1,1,1,1…… The limit of 1