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Math and science::Analysis::Tao::07. Series

Geometric series

Let \( x \) be a real number. If \( |x| \ge 1 \), then the series \( \sum_{n=0}^{\infty} x^n \) is divergent. If however \( |x| \le 1 \), then the series is absolutely convergent and the sum is given by:

On the reverse side, there is some geometric visual reasoning; can you remember what it looks like?