turkey-yks 2015 Q33

turkey-yks · Other · lys1-math Geometric Sequences and Series Fractal/Iterative Geometric Construction (Area, Length, or Perimeter Series)
In the rectangular coordinate plane, isosceles triangles are drawn with base vertices at consecutive even natural numbers on the x-axis and apex on the curve $y = 2 ^ { - x }$.
Accordingly, what is the sum of the areas of all the triangles drawn in square units?
A) $\frac { 3 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 4 } { 3 }$
D) 1
E) 2 
In the rectangular coordinate plane, isosceles triangles are drawn with base vertices at consecutive even natural numbers on the x-axis and apex on the curve $y = 2 ^ { - x }$.

Accordingly, what is the sum of the areas of all the triangles drawn in square units?\\
A) $\frac { 3 } { 2 }$\\
B) $\frac { 2 } { 3 }$\\
C) $\frac { 4 } { 3 }$\\
D) 1\\
E) 2
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