find-the-sum-of-the-infinite-series-tan-1-2-n-2- Tinku Tara June 4, 2023 Trigonometry 0 Comments FacebookTweetPin Question Number 30235 by NECx last updated on 18/Feb/18 findthesumoftheinfiniteseriestan−1(2n2) Commented by prof Abdo imad last updated on 18/Feb/18 forn⩾12n2=n+1−(n−1)1+(n+1)(n−1)letputn=tanun2n2=tanun+1−tann−11+tanuntanun−1=tan(un+1−un−1)arctan(2n2)=un+1−un−1andSN=∑n=1Narctan(2n2)=∑n=1N((un+1−un)+(un−un−1))=∑n=1N(un+1−un)+∑n=1N(un−un−1)=uN+1−u1+uN−u0=arctan(N+1)+arctanN−π4limN→∞SN=π2+π2−π4=3π4. Commented by abdo imad last updated on 18/Feb/18 arctanmeanstan−1. Commented by NECx last updated on 19/Feb/18 thankyousomuch Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-x-such-that-x-3-mod5-x-5-mod7-x-7-mod11-Next Next post: Question-95773 Leave a Reply Cancel replyYour email address will not be published.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.