WOLFRAM|DEMONSTRATIONS PROJECT

Geometric Series

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step
3
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0
A geometric series is an infinite sum of the form
r+
2
r
+
3
r
+…
(often the series starts with 1). In this Demonstration the ratio
r=
1
2
, so this sum is
1
2
+
1
4
+
1
8
+…
, which sums to 1. Zoom in to see that there is always a gap between any partial sum and 1. Zooming in too far shows no terms on the right.