Given distinct straight lines OA and OB. From a point in OA a perpendicular is drawn to OB; from the foot of this perpendicular a line is drawn perpendicular to OA. From the foot of this second perpendicular a line is drawn perpendicular to OB; and so on indefinitely. The lengths of the first and second perpendiculars are a and b, respectively. Then the sum of the lengths of the perpendiculars approaches a limit as the number of perpendiculars grows beyond all bounds. This limit is:
(A)\ \frac {b}{a \minus{} b} \qquad (B)\ \frac {a}{a \minus{} b} \qquad (C)\ \frac {ab}{a \minus{} b} \qquad (D)\ \frac {b^2}{a \minus{} b} \qquad (E)\ \frac {a^2}{a \minus{} b} trigonometryratiogeometric sequence