Given a square ABCD with side length equal to 'a'. From side AB, draw a line extending from point B in the opposite direction of point A, and place point B1 on the line continuing from side AB where AB1 = AC. Use the concatenated side BB1 to create a square BB1C1D1. Then, from side BB1, draw a line extending from point B1 in the opposite direction of point B, and place point B2 on the line connecting from this side BB1, where BB2 = BC1. Given point B1, B2, B3, ... As described above, find the sum of the lengths of the line segments AB, BB1, B1B2, ... Please show your work too — thanks!
Topic: Infinite Geometric Series