let-f-x-x-1-x-1-1-calculate-f-n-2-2-if-f-x-n-0-a-n-x-2-n-find-the-sequence-a-n- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 42999 by abdo.msup.com last updated on 06/Sep/18 letf(x)=x+1x−11)calculatef(n)(2)2)iff(x)=∑n=0∞an(x−2)nfindthesequencean Commented by maxmathsup by imad last updated on 08/Sep/18 1)firstletfindf(n)(x)wehavef(n)(x)=(x)n+(1x−1)nbut{1x−1}(n)=(−1)nn!(x−1)n+1letdetermine(x)n={x12}(n)letαfromQ{xα}(1)=αxα−1⇒{xα}(2)=α(α−1)xα−2⇒{xα}(n)=α(α−1)…(α−n+1)xα−nso{x12}(n)=12(12−1)(12−2)….(12−n+1)x12−n=12(−12)(−32)….(1−2n+2)2)x12−n=12(−12)(−32)….(−2n−32)x12−n⇒f(n)(x)=12(−12)(−32)=(−2n−32)x12−n+(−1)nn!(x−1)n+1.⇒f(n)(2)=12(−12)(−32)…..(−2n−32)212−n+(−1)nn!=12n2(−12)(−32)…(−2n−32)+(−1)nn!.2)developpementoff(x)atintegrserieserisatv(2)givef(x)=∑n=0∞f(n)(2)n!(x−2)n⇒an=f(n)(2)n!⇒an=1(n!)2n2(−12)(−32)…(−2n−32)+(−1)n.nt Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Dear-Jr-inter-students-use-this-firmulas-Derivates-d-dx-constant-k-0-d-dx-x-n-n-x-n-1-d-dx-x-2-2x-d-dx-Next Next post: Question-174069 Leave a Reply Cancel replyYour email address will not be published.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.