(D There's a well known allegory about the famous mathematician, Gauss (read: some very dead, old white guy), who, as an elementary school student, was asked by his teacher to add 1 to 100, in attempt to keep him busy for a while. Gauss, being the burgeoning mathematician he was, gured it out very quickly with the following trick: 1+2+...+99+ 100 could be sorted into 50 pairs, each adding to 101: (1+100) + (2+99) +...+ (49+52) + (50+51) = (50)101 = 5050 In this question, we will walk through a similar proof to show exactly where one of our mysterious summation equations comes from: Consider 2;; i, the formula we needed in class. We can align double this sum as: 2i= i=1 2i=[1+2+...+(n1)+n] i=1 +[n+(n1)+...+2+1] (a) Add down each column in the brackets to show that you get \" _ pairs of numbers adding to _ \" (ll in the blanks in your explanation), and immediately get that the sum has to be the product of numbers in those \"blanks\". (b) Solve for 23:11' in terms of 71. Your result should be our formula from class