Final answer:
The question seems to ask for a transformation of the sequence x[n], but the information is incomplete. A provided proof shows the sum of the first n odd numbers equals n² by rearranging terms.
Step-by-step explanation:
The student has provided a finite sequence x[n] = {4,5,-2,3,-1,-3,0,2,-4} defined for indices from -4 ≤ n ≤ 4. Unfortunately, without the operations or transformations the student wants to apply to this sequence to obtain new sequences, we cannot determine the values for n¹, n², … , n⁶. If more information is given about how to transform the original sequence x[n], we can proceed with finding these values.
If we consider the provided information n terms that the expression in the box is = n², and follow the instructions, which describe a method to prove that the sum of odd numbers from 1 to (2n - 1) is equal to n². This is done by manipulating the series and repeatedly adding terms from the end of the series to the beginning.
Illustrating the provided series manipulation: the sum of first n odd numbers can be expressed as 1 + 3 + 5 + ... + (2n - 3) + (2n - 1). By applying the steps mentioned, we're showing that this series can be transformed to yield 2n², which after dividing by 2 gives us n².