[Value = 9 points]
Let AOB be an acute angle, and Let C be a point on OA. From C, a perpendicular is drawn to OB, meeting OB at point D. The length of CD is a. From D, a perpendicular is drawn to OA, meeting OA at E. The length of DE is b. From E, a perpendicular is drawn to OB. From the base of this perpendicular, a perpendicular is drawn to OA. This procedure is repeated infinitely many times. What is the sum of the lengths of the perpendiculars dawn?
