# 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