given-two-sequence-a-n-gt-0-b-n-gt-0-such-n-N-a-n-n-lt-b-n-lt-a-n-1-n-a-if-n-1-a-n-converge-then-n-1-b-n-converge-b-proof-that-if-a-n-0-1-then-b-n-0-1-c- Tinku Tara June 3, 2023 Limits 0 Comments FacebookTweetPin Question Number 676 by 123456 last updated on 22/Feb/15 giventwosequencean>0,bn>0such∀n∈N∗,ann<bn<an1/na.if∑+∞n=1anconvergethen∑+∞n=1bnconverge?b.proofthatifan∈(0,1)thenbn∈(0,1)c.(dis)proofthatifan→1thenbn→1 Commented by prakash jain last updated on 22/Feb/15 b.0<an<1⇒0<ann<10<an<1⇒0<an1/n<1ann<bn<an1/n⇒0<bn<1c.∵an→1⇒ann→1andan1/n→1∴an→1⇒bn→1a.Ifanconvergeswecansayannconverges.butwecannotconcludeanythingaboutan1/n.Hencewecannotconcludethatbnonverges. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-131745Next Next post: Question-131751 Leave a Reply Cancel replyYour email address will not be published.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.