the infimum is when $n=1$, infimum is $-1$ the supremum is when $n=2$, supremum $1+\frac{1}{2}=\frac{3}{2}$
I need help to understand this part:
over the set $n \geq m$, the infimum is $\frac{-1}{2k+1}$ where $2m-1=2(2k+1)-1=4k-1$
or $2m+1=4k-1$
when $m \rightarrow ∞, k \rightarrow ∞$, so the infimum is tending to $0$
So the limit inferior is $0$
My problem is I do not know how to put it in notation of limit
over the set $n \geq m$, the supremum is $1+\frac {1}{2k}$ where $2m=4k$ or $2m+2=4k$
when when $m \rightarrow ∞, k \rightarrow ∞$, so the supremum decreases to $1$
So the limit superior is $1$ thanks for your help