Limit of sum of lengths
Source:
January 12, 2009
trigonometryratiogeometric sequence
Problem Statement
Given distinct straight lines and . From a point in a perpendicular is drawn to ; from the foot of this perpendicular a line is drawn perpendicular to . From the foot of this second perpendicular a line is drawn perpendicular to ; and so on indefinitely. The lengths of the first and second perpendiculars are and , 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}