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Power versus exponential

Published online by Cambridge University Press:  01 August 2016

P. Shiu
P. Shiu*
Affiliation:
Department of Mathematics, Loughborough University of Technology, Leicestershire, LE11 3TU
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Extract

Let k be a positive integer and a > 1. It is well known that

.

The shortest proof seems to be the following. By estimating the exponential function with only one term from its series we see at once that

.

Type
Research Article
Information
The Mathematical Gazette , Volume 73 , Issue 463 , March 1989 , pp. 25 - 28
Copyright
Copyright © The Mathematical Association 1989

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References

1. Goodstein, R.L., A note on convergence, Math. Gaz. 38, 140–141 (1954).Google Scholar
2. Watson, G.N., A note on convergence, Math. Gaz. 39, 297–299 (1955).Google Scholar