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Proof Without Words: From Floor to Stairs

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Proof Without Words:

From Floor to Stairs

J ULIJE J AKS ˇETIC´

W W e present a geometric interpretation of the identity

1

X

1

k¼1

r k j k

2

¼ X

1

k¼1

ð2k 1Þ r k j k

:

Julije Jaksˇetic´

Faculty of Food Technology and Biotechnology, Section for Mathematics

Pierottijeva 6 10000 Zagreb Croatia

e-mail: jjaksetic@pbf.hr

1This identity can be found in many books on elementary number theory. The earliest mention appears to be in M. A. Heaslett and J. V. Uspensky,Elementary Number Theory, McGraw-Hill, 1939 (Problem 10, p. 98).

Ó2021 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature, Volume 43, Number 3, 2021 29

https://doi.org/10.1007/s00283-021-10111-8

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