I am asked to find the supremum and infimum of the set $$\left\{\left.1 +\frac{(-1)^n}n\;\right|\;n\in\Bbb N\right\}\subset\Bbb R.$$ What I first did was separated it in to cases and found that when $n$ is even, we get $1 +\frac{1^n}n$, and when $n$ is odd we get $1 -\frac{1^n}n$. I am lost from here. The book says the infimum is zero which I can understand I think, but I am not sure how they got $3/2$ as the supremum. All the help would be appreciated.
Note: I am learning to type math in to here so my apologies for not doing it for the set above.
