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Math 163 Information and Links
Click Here for a link to contact information for your instructor.
Click Here
for the current Math Schedule to see the times courses are offered.
Check out these links which geometrically
illustrate the convergence of series. The pictures show a fixed area broken up into
pieces repeatedly.
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This shows that 1/3 + 1/9 +
... = 1/2. Notice how the large square is split into three pieces
vertically. Then the middle piece is split into 3 pieces horizontally.
Red and Yellow each take up one third of each area. The sum of each of
those pieces fills up the square. Since the area of the square can be
split into two congruent pieces (the one for yellow and the one for red), then
the area occupied by each color must be 1/2.
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This shows that 1/4 +
1/16 + ... = 1/3. A similar argument to the one above. Here a
triangle is split into 4 congruent pieces. One color occupies each large
piece, with one large piece then split into 4 again. The total area of
the triangle is split into 3 congruent pieces which added together give the
area of the original triangle. Therefore, each one must occupy 1/3 of
the area.
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