[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-460862-105":59,"doc-detail-460862-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","ap-calc-bc-convergence-practice-series-test-practice","AP Calc BC Convergence Practice - Series Test Practice","","A practice set for AP Calculus BC focused on determining convergence of various infinite series, especially alternate series and power-series-like expressions. Problems require students to find values of parameters for convergence, justify convergence or divergence, determine intervals of convergence, and apply error bounds for partial sums. Several items also ask for practical stopping criteria such as the number of terms needed to make the error smaller than a specified tolerance.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ap-calc-bc-convergence-practice-series-test-practice/460862/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ap-calc-bc-convergence-practice-series-test-practice/460862.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do I determine values of p so an alternate series converges?","Question",{"text":112,"@type":113},"Use the alternating-series convergence conditions: identify when the terms decrease in magnitude to 0, and then state the appropriate p range for convergence.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"When partial sums approximate the true sum, how is the error bound determined?",{"text":117,"@type":113},"For a decreasing alternate series, the maximum error is tied to the magnitude of the next term. Compare that bound to the next-term expression to control the approximation.",{"name":119,"@type":110,"acceptedAnswer":120},"How do I find the complete interval of convergence for a series with parameter k?",{"text":121,"@type":113},"Apply the relevant convergence test (commonly ratio/root test for power-series forms) to find which x values satisfy convergence, then include endpoints based on separate checks.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},460862,1790759894,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":52,"preview_page_count":4},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","AP Calc BC Convergence Practice Name: Block: Seat:  \n1. Determine what values of p so that this is a converging alternate series.  \n1X (~~ ~~1n)n  \nn=1  \n2. Consider  \n1X (~~ ~~􀀀1n2)n  \nn=1  \n(a) If you added up the 􀀌rst six terms, what is the di􀀋erence between the partial sum and the actual sum? Since this is a decreasing series, isn't the maximum possible error related to the next term? What is the error bound ?  \n(b) Since (approximation + error = actual value), is this an overestimate or an underestimate of the sum?  \n(c) How many terms before the error is less than 0:01?  \n3. (1969 BC 45) What is the complete interval of convergence of  \n (x~~ ~~+k21)k  \nSt. Francis High School AP Calc BC  \nPage 2 of 4 2015  \nFrom 1973 BC 19  \n4. Justify why the series converges or not  \n 1n2  \n5. Justify why the series converges or not  \n1X 1n  \nn=1  \n6. Justify why the series converges or not  \n (~~ ~~􀀀1~~p n~~)n  \nFrom 1988 BC 44  \n7. Justify why the series converges or not 1X(􀀀1)n+1 2nn=1  \n8. Justify why the series converges or not  \n1 X  \nn=1  \n1 n  \n􀀒 32 􀀓 n  \nSt. Francis High School Page 2 of 4 AP Calc BC  \nPage 3 of 4  \n9. Justify why the series converges or not  \n n~~ ~~l1nn  \nFrom 1988 BC 30  \n10. 1  \nXi=n  \n2015  \n􀀒 13 􀀓 i =  \nFrom 1993 BC 16  \n11. Justify why the series converges or not  k~~ ~~2~~ ~~  \n12. Justify why the series converges or not  \n1 X  \nk=1  \n􀀒 67 􀀓  \nk  \nSt. Francis High School Page 3 of 4 AP Calc BC  \nPage 4 of 4 2015  \n13. Justify why the series converges or not  \n1X (~~ ~~􀀀1)kk  \nk=2  \nFrom 1997 BC 76  \n14. Justify why the series converges or not  \n􀀚 2n5~~ ~~1 􀀛  \n15. Justify why the series converges or not  \n􀀚 enn 􀀛  \n16. Justify why the series converges or not  \n􀀚 1~~ ~~nen 􀀛  \n)set anretla regnol on si ht 0 \u003C p m eht etoN( seireS gnitanretlA yb 1 > p . 1  \n. eta mitser evo na si smret xis tsr 􀀌 eht fo mus e ht os , evita gen si 19 = 7a mret htneves ehT . 194 􀀔 j nS 􀀀 Sj red nia meR e hT . 2  \n. dede en s mr et 1 1 os , 1 0. si mret htnet eh T 1 k) 1 􀀀(  \n] 0 2 􀀀[ os ~~ ~~ r of seires-p ; ~~ ~~ tset ot T SA ne ht ) 0 ; 2 􀀀( te g ot tset oitar es U . 3  \n; 2k 2k  \nsegrevnoc 0 = na mil d na s esa er ced , set anretla ylt cirts : TSA. 6 , egrevid 1 = p . 5 , egrevnoc 1 > p . 4 segrevid , seires-p 1 = p , ci nomrah . 8 ;segrevnoc 0 = na mil d na s esa er ced , set anretla ylt cirts : TSA . 7 segrevid , skrow 1n htiw nosira pm oc t cerid , 1 = mil sliaf tset oitar , 0 = mil sliaf tset mret-h tn . 9 n 􀀓 13 􀀒 32 . 0 1  \nsegrevnoc na T CD yb os , seires-p tne grevnoc a si hcih w 22k = nb tel . 1 1  \ncino mr ah ci nomrah .tla tn egrevnoc . 3 1 ;segrevnoc , 1 \u003C r cirt emo eg . 2 1  \nSt. Francis High School Page 4 of 4 AP Calc BC","cbCaihiyXP6t4YpF","https://ap.wps.com/l/cbCaihiyXP6t4YpF","pdf",116737,"English","# Convergence Practice\n## Alternate series parameter selection\n## Partial sum and error estimation\n## Interval of convergence\n## Convergence/divergence justifications\n## Parameter-based convergence tests","[{\"question\":\"How do I determine values of p so an alternate series converges?\",\"answer\":\"Use the alternating-series convergence conditions: identify when the terms decrease in magnitude to 0, and then state the appropriate p range for convergence.\"},{\"question\":\"When partial sums approximate the true sum, how is the error bound determined?\",\"answer\":\"For a decreasing alternate series, the maximum error is tied to the magnitude of the next term. Compare that bound to the next-term expression to control the approximation.\"},{\"question\":\"How do I find the complete interval of convergence for a series with parameter k?\",\"answer\":\"Apply the relevant convergence test (commonly ratio/root test for power-series forms) to find which x values satisfy convergence, then include endpoints based on separate checks.\"}]","AP Calc BC Convergence Practice - Series Test Practice | PDF"]