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A Converging Geometric Series
A Converging Geometric Series
This Demonstration shows that =+++…+=1.
∞
∑
n=1
n
1
2
1
2
1
4
1
8
n
1
2
The square is half empty with area when . The square is empty at . In general, the square is empty at step and +++…+ full, which shows that converges to 1.
1
2
n=1
1
4
n=2
n
1
2
n
1
2
1
4
1
8
n
1
2
∞
∑
n=1
n
1
2