Final answer:
The operation described manipulates an array of integers to transform its size, which relates to the computation of the median of a sequence of numbers depending on whether the total count is even or odd.
Step-by-step explanation:
The question revolves around an operation on an array of integers which can be described as a transformation reducing the array's size by one. Every move consists of picking two different elements, removing them, and then appending their sum to the end of the array. This process is related to calculating the median when ordering this array of numbers.
Regarding the calculation of the median, when n is an odd number, it is simply the middle value after the data has been ordered. If n is an even number, the median is the average of the two middle values. The mathematical representations provided suggest manipulations of series to simplify or represent sums of integers as formulas that are useful in this context.