let-A-n-k-0-n-1-sin-kpi-2n-and-B-n-k-0-n-1-cos-kpi-2n-1-find-A-n-and-B-n-interms-of-n-2-calculate-lim-n-A-n-B-n-3-calculate-lim-n-A-n-lim-n- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 47857 by maxmathsup by imad last updated on 15/Nov/18 letAn=∑k=0n−1sin(kπ2n)andBn=∑k=0n−1cos(kπ2n)1)findAnandBnintermsofn2)calculatelimn→+∞AnBn3)calculatelimn→+∞Anlimn→+∞Bn. Commented by maxmathsup by imad last updated on 17/Nov/18 wehaveBn+iAn=∑k=0n−1eikπ2n=∑k=0n−1(eiπ2n)k=1−eiπ21−eiπ2n=1−i1−cos(π2n)−isin(π2n)=1−i2sin2(π4n)−2isin(π4n)cos(π4n)=1−i−2isin(π4n)(cos(π4n)+isin(π4n))=i+12sin(π4n)e−iπ4n=1+i2sin(π4n){cos(π4n)−isin(π4n)}=cos(π4n)−isin(π4n)+icos(π4n)+sin(π4n)2sin(π4n)⇒Bn=cos(π4n)+sin(π4n)2sin(π4n)=12tan(π4n)+12An=cos(π4n)−sin(π4n)2sin(π4n)=12tan(π4n)−122)wehaveAnBn=cos(π4n)−sin(π4n)cos(π4n)+sin(π4n)∼1−π232n2−π4n1−π232n2+π4n→1(n→+∞)⇒limn→+∞AnBn=1. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 1-find-x-arctan-x-dx-2-find-the-value-of-0-1-x-arctan-x-dx-Next Next post: Anyone-know-how-it-came-to-the-working-equation- Leave a Reply Cancel replyYour email address will not be published.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.