If M_k = [[k, k-1],[k-1, k]] where k is a natural number, then what is |M_1|+|M_2|+|M_3|+...+|M_50| equal to?

The determinant of M_k = k² - (k-1)² = 2k - 1. So the sum is Σ(2k-1) for k=1 to 50 = 2(1+2+...+50) - 50 = 2(1275) - 50 = 2550 - 50 = 2500. This is the sum of the first 50 odd natural numbers, which equals 50² = 2500.