Consider the figure shown below. The right triangle ABC has legs of length a and b, a

Question

Consider the figure shown below.  The right triangle ABC has legs of length a and b, a<b.  From the right angle at C a perpendicular is drawn to the hypotenuse at B_1.  A second perpendicular is drawn from B_1 to CA meeting at C_1.  The process, conducted indefinitely generates line segment lengths y_1, y_2, y_3,...y_n,...
a. Find y_1 in terms of a and b.
b. Find x in terms of a and b.
c.  Find a recurrence relation for y_n

anonymous · Answer

d. Determine $$\sum_{i=1}^{\infty}y _{i}$$

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e.  If a=3 and b=4, what is the value of $$\sum_{i=0}^{\infty}y _{i}?$$

anonymous · Answer

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