**Visualising Infinite Sums as a Study in Shifts of Attention**

**John MASON**

#### Open University & University of Oxford

United Kingdom

Published in The Mathematician Educator, 2021, Vol 2, No. 1, pp 11-32.

### Abstract

A method of depicting the sum of finite and infinite geometric progressions with ratio at most 1/2 is extended in various ways to deal with ratios greater than 1/2, and generalised for use with other infinite series. The point is not so much to provide ‘proofs without words’, as to provide a domain of tasks which include opportunities to catch how the focus and form of attention shifts in order to interpret sequences of diagrams mathematically. Applets which enable the user to explore variations and generate examples for themselves are available.

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