let-u-n-0-1-x-n-sin-pix-dx-1-prove-that-u-n-converges-2-prove-that-u-n-0-pi-sint-t-dt- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 32042 by abdo imad last updated on 18/Mar/18 letun=∫01xnsin(πx)dx1)provethatΣunconverges2)provethatΣun=∫0πsinttdt. Commented by abdo imad last updated on 20/Mar/18 letputSn=∑k=0n∫01xksin(πx)dxSn=∫01(∑k=0nxk)sin(πx)dx=∫011−xn+11−xsin(πx)dx⇒Sn−∫01sin(πx)1−xdx=−∫01xn+11−xsin(πx)dxand∃m>0/∣Sn−∫01sin(πx)1−xdx∣⩽m∫01xn+1dx=mn+2→n→∞0⇒SnconvergedandlimSn=∫01sin(πx)1−xdx2)ch.1−x=tgive∫01sin(πx)1−xdx=∫01sin(π(1−t))t=dt=∫01sin(πt)tdtafterch.πt=ugivelimn→∞Sn=∫0πsin(u)uπduπ=∫0πsinuudu.so∑n=0∞un=∫0πsinuudu. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-the-nature-of-u-n-u-n-1-2-n-n-3-Next Next post: d-2-y-dx-2-ytan-x-e-x-y-0-1-y-0-0- Leave a Reply Cancel replyYour email address will not be published.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.