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CRITERIA FOR THE SEQUENCE OF DIFFERENCES OF A BOUNDED SEQUENCE TO BE NULL
Part of
- Convergence and divergence of infinite limiting processes
DAVID BORWEIN
Journal:

Bulletin of the Australian Mathematical Society / Volume 88 / Issue 1 / August 2013

Published online by Cambridge University Press:

17 September 2012, pp. 123-127

Print publication:

August 2013
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Conditions are established for the sequence of differences $\{a_n-a_{n-1}\}$ of a bounded sequence $\{a_n\}$ of complex terms to converge to zero when a certain linear nonhomogeneous difference expression of the form $k_0 a_n+k_1a_{n-1}+\cdots +k_na_0$tends to zero as$n\to \infty .$