find-n-1-1-n-n-cos-nx-and-n-1-1-n-n-sin-nx- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 38942 by math khazana by abdo last updated on 01/Jul/18 find∑n=1∞(−1)nncos(nx)and∑n=1∞(−1)nnsin(nx) Commented by prof Abdo imad last updated on 09/Jul/18 letf(x)=∑n=1∞(−1)nncos(nx)f(x)=Re(∑n=1∞(−1)nneinx)=Re(w(x))w(x)=∑n=1∞(−eix)nn=−ln(1+eix)(Σznn=−ln(1−z))butln(1+eix)=ln(1+cosx+isinx)=ln(2cos2(x2)+2isin(x2)cos(x2))=ln(2)+ln(cos(x2)eix2)=ln(2)+ln(cos(x2))+ix2⇒w(x)=−ln(2cos(x2))−ix2⇒f(x)=−ln(2cos(x2))alsoweget∑n=1∞(−1)nnsin(nx)=−x2. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: verify-that-the-force-F-xyi-xyj-yzk-is-conservative-Next Next post: lim-x-pi-2-1-sin-pi-2x-5-sin-x-pi-2-ln-4-cos-pi-2x-1-pi-2-x-2- Leave a Reply Cancel replyYour email address will not be published.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.