Question-29-Theres-2-same-ratio-sequences-a-n-b-n-with-a-ratio-of-non-zero-And-if-two-sums-of-each-sequences-n-1-a-n-n-1-b-n-are-convergent-and-two-equations-n-1-a-n-b Tinku Tara November 2, 2024 Others 0 Comments FacebookTweetPin Question Number 213298 by MathematicalUser2357 last updated on 02/Nov/24 Question29.Theres2same−ratiosequences{an},{bn}witharatioofnon−zeroAndiftwosumsofeachsequences(∑∞n=1an,∑∞n=1bn)areconvergent,andtwoequations∑∞n=1anbn=(∑∞n=1an)×(∑∞n=1bn)and3×∑∞n=1∣a2n∣=7×∑∞n=1∣a3n∣aretrue.If∑∞n=1b2n−1+b3n+1bn=S,thenFindthevalueof120S.(koreauniversityexamquestion) Answered by MrGaster last updated on 02/Nov/24 ∑∞n=1an=a11−ra,∑∞n=1bn=b11−rb∑∞n=1anbn=a1b11−rarba1b11−rarb=a11−ra⋅b11−rb3∑∞n=1∣a2n∣=7∑∞n=1∣a3n∣3∣a1∣ra1−ra2=7∣a1∣ra21−ra33(1−ra3)=7(1−ra2)3−3ra3−7ra2+4=0(ra−1)(3ra2−4ra−4)=0ra=1,ra=2,ra=−23ra=1doesnotsatisfythecondlitionforconvergence.since∣ra∣<1,havera=−23.∑∞n=1b2n−1+b3n+1bn=∑∞n=1(b1rb2n−2+b1rb3nb1rbn−1)=∑∞n=1(rb2n−2+b1rb3nrbn−1)=∑∞n=1(rbn−1+rb2n+1)=∑∞n=1rbn−1+∑∞n=1rb2n+1=11−rb+rb3(1−rb)(1+rb)=1+rb+rb31−rb2=1+rb+rb3(1−rb)(1+rb)=1+rb+rb31−rb2Giventhat120S=120(1+rb+rb31−rb2).lfrb=−23120S=120(1−23+(−23)31−(−23)2)=120(1−23−8271−49)=120(27−18−82759)=120(12758)=120(127⋅95)=120⋅115=8 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 0-x-x-2-x-3-x-2018-1-x-2021-dx-Next Next post: Question-213330 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.