Resolution of grandi’s paradox and investigations on related series

Serdar Beji*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Grandi’s paradox is resolved by introducing a consistent truncation concept for series expansions of Grandi-type functions. In addition, a convergence improvement technique by successive averaging of truncated series of subsequent orders is presented. Resulting rectified series expansions satisfy certain critical points exactly and represent the corresponding generating functions considerably better compared to standard expansions. Finally, successive averages together with collocation technique are applied to series expansions of arbitrarily selected functions for demonstrating the improvements in series representations.

Original languageEnglish
Pages (from-to)265-277
Number of pages13
JournalApplied Mathematics E - Notes
Publication statusPublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Hampstead Psychological Associates. All rights reserved.


Dive into the research topics of 'Resolution of grandi’s paradox and investigations on related series'. Together they form a unique fingerprint.

Cite this