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A proof of the “Theorem of the Means.”

Published online by Cambridge University Press:  31 October 2008

C. E. Walsh
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Numerous proofs have been given of this familiar theorem, which states that if a1, a2, …, an are positive, and not all equal, then

The following is an elementary proof by induction, which I have not seen used before. It is, of course, not claimed to be novel, and not likely to be so.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 33 , January 1943 , pp. 17 - 18
Copyright
Copyright © Edinburgh Mathematical Society 1943

References

1 See e.g. Hardy, Littlewood & Pölya Inequalities, where many references will be found.