So I'll begin by stating I'm only referencing another post on the blog beacuse something still doesn't make sense and my comment on that post hasn't been responded. Therfore full credit isn't mine.
This is the question: Resizing an array by a non-constant, continually , posted originally by Noy.
I would like to refer to Noah Carter's answer:
This can be easily shown using the Accounting Method. Consider an array of size k+sqrt(k) such that the first k entries are occupied and the rest sqrt(k) are empty. Let us make Insert-Last operation draft sqrt(k)+2 coins: One will be used to pay for insertion while the rest (sqrt(k)+1 coins) will be deposited and used for credit. From here, execute Insert-Last sqrt(k) times. We shall then have k+sqrt(k) credit coins: in total we had drafted k+2sqrt(k) coins, sqrt(k) of which we used for paying for the insertions. Hence, we won't need to pay for the resizing of the array. As soon as the array gets full, we would be able to utilize our k+sqrt(k) credit coins and pay for the resizing operation. Since k = Θ(n), each Insert-Last operation drafts sqrt(k)+2 = O(sqrt(k)) = O(sqrt(n)) coins and thus takes O(sqrt(n)) amortized.
So, I understand how this would give me a bound from above for a series of n Insertions but assuming I have a series of n Retrieves for example than why am I bounded from below by nsqrt(n) and not by n?