The vertices of a polygon are:

$\displaystyle (-1,0), \ (-1+2^{-n},1-(-1+2^{-n})^{2}), \ (-1+2 \cdot 2^{-n},1-(-1+2\cdot2^{-n})^{2}), \ (-1+3\cdot2^{-n},1-(-1+3\cdot2^{-n})^{2}), ...,(1,0)$

I have to show that the area of the polygon is 1 + 4^(-1) + 4^(-2) + ... + 4^(-n).

How would I go about doing that? Not sure how to proceed.