O(1) Amortized + O(k) = O(k) Amortized?

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My professor made the following claim:

O(1) Amortized + O(k) = O(k) Amortized

I agreed with him at first but giving it deep thinking I think it's wrong, why?

O(1) Amortized means every k operations are done in O(k) so O(1) Amortized = O(k) Worst.

From here we can conclude: O(1) Amortized + O(k) = O(1) + O(k) = O(k) Amortized

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