{"paper":{"title":"A Dilution Test for the Convergence of Subseries of a Monotone Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lasse Leskel\\\"a, Mikko Stenlund","submitted_at":"2010-11-17T20:22:41Z","abstract_excerpt":"Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It is natural to ask whether the converse is also true: Is it possible to determine the convergence of an arbitrary subseries of a monotone series by looking at a suitably weighted version of the original series? In this note we show that the answer is affirmative and introduce a new convergence test particularly designed for this purpose."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4697","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}