This is a short, animated visual proof computing the sums of the series of reciprocals of specific binomial coefficients, namely those obtained by considering one column in Pascal's triangle. Amazingly, the same geometric argument, relying on telescoping, will give a nice formula for the infinite sum of reciprocals of each column.
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For a related video showing just one column, see this video:
• Infinite series: summi...
This animation is based on a visual proof by Tom Edgar from the June 2016 issue of Mathematics Magazine (www.jstor.org/... page 212-213 ).
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14 окт 2024
