{"id":"https://openalex.org/W2280611643","doi":"https://doi.org/10.1080/00029890.2017.1416875","title":"The Error in an Alternating Series","display_name":"The Error in an Alternating Series","publication_year":2018,"publication_date":"2018-03-22","ids":{"openalex":"https://openalex.org/W2280611643","doi":"https://doi.org/10.1080/00029890.2017.1416875","mag":"2280611643"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2017.1416875","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2017.1416875","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.08568","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057703440","display_name":"Mark B. Villarino","orcid":null},"institutions":[{"id":"https://openalex.org/I31944674","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51","country_code":"CR","type":"education","lineage":["https://openalex.org/I31944674"]}],"countries":["CR"],"is_corresponding":true,"raw_author_name":"Mark B. Villarino","raw_affiliation_strings":[",","Escuela de Matem\u00e1tica, Universidad de Costa Rica, 11501 San Jos\u00e9, Costa Rica mark.villarino@ucr.ac.cr"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Escuela de Matem\u00e1tica, Universidad de Costa Rica, 11501 San Jos\u00e9, Costa Rica mark.villarino@ucr.ac.cr","institution_ids":["https://openalex.org/I31944674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057703440"],"corresponding_institution_ids":["https://openalex.org/I31944674"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00344745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"125","issue":"4","first_page":"360","last_page":"364"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9447000026702881,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9447000026702881,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9049000144004822,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.766568124294281},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6226894855499268},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5655674934387207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5025050640106201},{"id":"https://openalex.org/keywords/alternating-series","display_name":"Alternating series","score":0.45966020226478577},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42141324281692505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22318968176841736},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.06558266282081604}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.766568124294281},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6226894855499268},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5655674934387207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5025050640106201},{"id":"https://openalex.org/C195597517","wikidata":"https://www.wikidata.org/wiki/Q438842","display_name":"Alternating series","level":3,"score":0.45966020226478577},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42141324281692505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22318968176841736},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.06558266282081604},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00029890.2017.1416875","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2017.1416875","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.08568","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.08568","pdf_url":"https://arxiv.org/pdf/1511.08568","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2280611643","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1511.08568.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1511.08568","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.08568","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.08568","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.08568","pdf_url":"https://arxiv.org/pdf/1511.08568","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323217","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W630607818","https://openalex.org/W1973871154","https://openalex.org/W2315418815","https://openalex.org/W2326064256","https://openalex.org/W2796644496","https://openalex.org/W4250228357","https://openalex.org/W4252553748"],"related_works":["https://openalex.org/W2776128341","https://openalex.org/W2102562169","https://openalex.org/W1980909683","https://openalex.org/W2078812553","https://openalex.org/W2168907009","https://openalex.org/W1773497522","https://openalex.org/W1030829794","https://openalex.org/W2511372611","https://openalex.org/W940655778","https://openalex.org/W2076445343","https://openalex.org/W2604749754","https://openalex.org/W2026690766","https://openalex.org/W3101037765","https://openalex.org/W2304140731","https://openalex.org/W91279522","https://openalex.org/W2005152329","https://openalex.org/W3183952296","https://openalex.org/W2390465865","https://openalex.org/W2971908675","https://openalex.org/W1500709119"],"abstract_inverted_index":{"We":[0,22],"give":[1,24],"a":[2,25],"new":[3,26],"proof":[4,27],"of":[5,10,18,28,34],"Johnsonbaugh's":[6],"refined":[7],"error":[8,30],"estimates":[9],"an":[11,16],"alternating":[12],"series":[13],"based":[14],"on":[15],"idea":[17],"R.":[19],"M.":[20],"Young.":[21],"also":[23],"the":[29,35],"estimate":[31],"and":[32],"convergence":[33],"Euler":[36],"transform.":[37]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}