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A note on sequences determined by a recurrence relation

Published online by Cambridge University Press:  20 January 2009

C. E. Walsh
C. E. Walsh
Affiliation:
Dublin
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§ 1. Copson and Ferrar have proved the following theorem:

Ifis a divergent series of positive terms, and (pn + qn) un−pnun−1 = ynalways, where yn → 0, then un → 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 2 , July 1932 , pp. 147 - 150
Copyright
Copyright © Edinburgh Mathematical Society 1932

References

page 147 note 1 Copson, and Ferrar, , Journal London Math. Soc., 4 (1929), 258–264.CrossRefGoogle Scholar See also Izumi, , Tôhoku Math. J., 33 (1931), 181–186.Google Scholar Further references will be found in these papers.

page 148 note 1 Knopp, K., “Theory and Application of Infinite Series” (1928), 72.Google Scholar