[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522693-105":59,"doc-detail-522693-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","infinite-geometric-series-determine-convergence-or-divergence-and-evaluate-series","Infinite Geometric Series - Determine Convergence or Divergence and Evaluate Series","","Algebra 2 worksheet focused on infinite geometric series problems. Students decide whether given geometric series converge or diverge by analyzing the first term and common ratio, then evaluate the infinite sums for series where the sum exists. Practice includes sequences written in numeric and variable forms and requires identifying convergence conditions, computing the common ratio, and applying the infinite geometric series sum formula to find S. Results are included for multiple items.",{"@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/infinite-geometric-series-determine-convergence-or-divergence-and-evaluate-series/522693/",{"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/infinite-geometric-series-determine-convergence-or-divergence-and-evaluate-series/522693.png","ImageObject",300,407,{"name":92,"@type":93},"Rhys","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you determine whether an infinite geometric series converges or diverges?","Question",{"text":112,"@type":113},"Use the common ratio r. The series converges when |r| \u003C 1, and diverges when |r| ≥ 1.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you evaluate an infinite geometric series once it converges?",{"text":117,"@type":113},"Apply the infinite geometric series sum formula using the first term a1 and the common ratio r to compute the value of S.",{"name":119,"@type":110,"acceptedAnswer":120},"What does it mean to determine the common ratio of an infinite geometric series?",{"text":121,"@type":113},"Compute r from the relationship between consecutive terms in the series, using a consistent ratio between successive terms or given expressions.","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},522693,1791710647,{"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":34,"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":143,"read_time":52,"preview_page_count":4},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Kuta Software-Infinite Algebra 2 Name   \nInfinite Geometric Series Date  Period   \nDetermine if each geometric series converges or diverges.  \n1) a 1 = −3, r = 4 2) a 1 = 4, r = − ~~ ~~34  \n3) a 1 = 5.5, r = 0.5 4) a 1 = −1, r = 3  \n5) 81 + 27 + 9 + 3..., 6) 7.1 + 17.75 + 44.375 + 110.9375...,  \n7) −3 + ~~ ~~125 − 4825 + ~~ ~~192125~~ ~~ ..., 8) 3128125 − ~~ ~~64625 + ~~ ~~32125 − ~~ ~~1625~~ ~~ ...,  \n9) k1 −4k − 1 10) k1 ~~ ~~169~~ ~~ (~~ ~~32)k − 1  \n∞ ∞ k − 1  \n11) Σi = 1 4.2 ⋅ 0.2 i − 1 12) k1 ~~ ~~76~~ ~~ (− ~~ ~~14)  \nEvaluate each infinite geometric series described.  \n 1  14) a 1 = 1, r = −4  \n13) a = 3 r = − 1 , 5  \n15) a 1 = 1, r = −3 16) a 1 = 1, r = ~~ ~~12  \n17) 1 + 0.5 + 0.25 + 0.125..., 9 27 81  \n18) 3 −  4 +  16 −  64  ...,  \n19) 81 − 27 + 9 − 3..., 20) 1 − 0.6 + 0.36 − 0.216...,  \n21) k1 5 ⋅ (− ~~ ~~15) k − 1 22) n1 −6 ⋅ (− ~~ ~~12)n − 1  \n∞ i − 1 ∞  \n23) Σi = 1 (~~ ~~13) 24) k1 4k − 1  \nDetermine the common ratio of the infinite geometric series.  \n25) a 1 = 1, S = 1.25 26) a 1 = 96, S = 64  \n16 28) a 1 = 1, S = 2.5  \n27) a 1 = −4, S = −  5   \nKuta Software-Infinite Algebra 2 Name   \nInfinite Geometric Series Date  Period   \nDetermine if each geometric series converges or diverges.  \n1) a 1 = −3, r = 4  \nDiverges  \n3) a 1 = 5.5, r = 0.5  \nConverges  \n5) 81 + 27 + 9 + 3..., Converges  \n7) −3 + ~~ ~~125 − 4825 + ~~ ~~192125~~ ~~ ..., Converges  \n9) k1 −4k − 1  \nDiverges  \n11) Σi 1 4.2 ⋅ 0.2 i − 1  \nConverges  \nEvaluate each infinite geometric series described.  \n13) a 1 = 3, r = − ~~ ~~15 5  \n2  \n15) a 1 = 1, r = −3  \nNo sum  \n2) a 1 = 4, r = − ~~ ~~34  \nConverges  \n4) a 1 = −1, r = 3  \nDiverges  \n6) 7.1 + 17.75 + 44.375 + 110.9375..., Diverges  \n8) 3128125 − ~~ ~~64625 + ~~ ~~32125 − ~~ ~~1625~~ ~~ ..., Diverges  \n10) k1 ~~ ~~169~~ ~~ (~~ ~~32)k − 1  \nDiverges  \n12) k1 ~~ ~~76~~ ~~ (− ~~ ~~14) k − 1  \nConverges  \n14) a 1 = 1, r = −4  \nNo sum  \n16) a 1 = 1, r = ~~ ~~12 2  \n17) 1 + 0.5 + 0.25 + 0.125..., 2  \n18) 3 − ~~ ~~94 + ~~ ~~2716 − ~~ ~~8164~~ ~~ ..., 12  \n7  \n19) 81 − 27 + 9 − 3...,  \n243  \n4  \n21) k1 5 ⋅ (− ~~ ~~15) k − 1 25  \n6  \ni 1 (~~ ~~13~~ ~~ )  \n23) Σ  \ni − 1  \n3  \n2  \n20) 1 − 0.6 + 0.36 − 0.216..., 0.625  \n22) n1 −6 ⋅ (− ~~ ~~12)n − 1  \n−4  \n24) k1 4k − 1  \nNo sum  \nDetermine the common ratio of the infinite geometric series.  \n25) a 1 = 1, S = 1.25 26) a 1 = 96, S = 64  \n0.2  1  \n−  \n2  \n27) a 1 = −4, S = − ~~ ~~165  \n 1  \n−  \n4  \n28) a 1 = 1, S = 2.5 0.6  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainM1PFGr7sik","https://ap.wps.com/l/cbCainM1PFGr7sik","pdf",35385,"English","# Determine if each geometric series converges or diverges\n# Evaluate each infinite geometric series described\n# Determine the common ratio of the infinite geometric series","[{\"question\":\"How do you determine whether an infinite geometric series converges or diverges?\",\"answer\":\"Use the common ratio r. The series converges when |r| \\u003c 1, and diverges when |r| ≥ 1.\"},{\"question\":\"How do you evaluate an infinite geometric series once it converges?\",\"answer\":\"Apply the infinite geometric series sum formula using the first term a1 and the common ratio r to compute the value of S.\"},{\"question\":\"What does it mean to determine the common ratio of an infinite geometric series?\",\"answer\":\"Compute r from the relationship between consecutive terms in the series, using a consistent ratio between successive terms or given expressions.\"}]","Infinite Geometric Series - Determine Convergence or Divergence and Evaluate Series | PDF",1791426068]