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I found this exercise on the internet:

find the supremum and infimum of the following set A1, where

A1 = {2(-1)^(n+1)+(-1)^((n^2+n)/2)(2+3/n): n belongs to |N*}

being |N* = |N\{0}

The solution was:

A1 = {-3, -11/2, 5}U{3/4k, -3/(4k+1),-4-3/(4k+2),4+3/(4k+3) : k belongs to |N*}

I don't get the reasoning behind. what's k? why and how did they use it?