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How Slowly can a Series Converge?

Published online by Cambridge University Press:  03 November 2016

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

Let f(x) (x≥0) be a positive continuous function. Associated with f(x), we can define a sequence of numbers {an} by setting an = f(n). Conversely, given any sequence of positive numbers {an}, we can find a positive continuous function f(x) such that f(n) = an. Of course, in this latter case, there is more than one such function f(x), but this is not relevant.

Type
Research Article
Information
The Mathematical Gazette , Volume 56 , Issue 398 , December 1972 , pp. 285 - 288
Copyright
Copyright © Mathematical Association 1972

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References

1. Hardy, G. H.: A Course of Pure Mathematics. Cambridge (10th edition, 1958).Google Scholar
2. Besicovitch, A. S. and Davies, Roy O.: Two Problems on Convex Functions. Math. Gaz., XLIX, NO. 367 (February 1965), pp. 66–9.Google Scholar