Don's new discovery about infinite series!
The figure below will work for any infinite geometric series.
We'll look at
Notice some things in the diagram above: The odd powers of 1/5 are tall
rectangles, and the even powers are squares, which makes sense. Don flipped the
picture above about the axis of symmetry of the big square..
If we now draw a line which
connects point A, the upper left corner of the big square, to the upper right
corner of each of the smaller squares at C and E, we hit the base of the big
square at F and form the triangle AFH.
This triangle will have an area which will be the sum of the infinite
Try to figure out why this works yourself.
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