Prove-that-for-all-complex-such-as-z-lt-1-n-1-z-n-z-n-1-2-n-1-nz-n-z-n-1-0- Tinku Tara June 4, 2023 Others 0 Comments FacebookTweetPin Question Number 89937 by ~blr237~ last updated on 20/Apr/20 Provethatforallcomplexsuchas∣z∣<1=∑∞n=1zn(zn−1)2+∑∞n=1nznzn−1=0 Commented by mathmax by abdo last updated on 20/Apr/20 wehavefor∣u∣<1∑p=0∞up=11−u⇒∑p=1∞pup−1=1(1−u)2u=zn⇒1(1−zn)2=∑p=1∞p(zn)p−1=∑p=1∞p(zp−1)n⇒∑n=1∞zn(zn−1)2=∑n=1∞zn∑p=1∞p(zp−1)n=∑p=1∞p∑n=1∞(z.zp−1)n=∑p=1∞p∑n=1∞zpnfromanotherside∑n=1∞nznzn−1=−∑n=1∞nzn∑p=0∞znp=−∑p=1∞pzp∑n=0∞zpn=−∑p=1∞p∑n=0∞zp(n+1)=−∑p=1∞p∑n=1∞zpn⇒∑n=1∞zn(zn−1)2+∑n=1∞nznzn−1=0 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-89928Next Next post: Prove-that-p-1-q-1-1-pq-p-q-1-pi-2-3- Leave a Reply Cancel replyYour email address will not be published.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.