Guess the answer to the first of the hard homework assignments in part 4 of the video, that is, sum the series 1 - 2^2 + 3^2 - 4^2 + 5^2 - based on the sequence of averages of averages of averages of the partial sums of this series. Base your guess on the first 5000 elements of this sequence calculated using Mathematica. Too devilish? Okay, here is some Mathematica code (just copy and paste into a Mathematica notebook) that you can modify and extend to calculate those 5000 elements (you only have to record the last few of those 5000 elements in your write-up). It calculates and prints the first 5000 elements of the sequence of averages of the partial sums of the series 1-1+1-1+ ClearAll Partialsum [0] = 0: For [i = 0, i