Question

Q4 20 Points Let (a.) 21 be a sequence of real numbers and a ER such that .-+ 4. No fles uploaded Q4.1 10 Points State the definition of " a Please select flies a ". Select files Q4.2 5 Points in 2020. Consider the sequence (6.) 1 given by bn = 24 in <2020 and be Using only the definition of convergence of sequences, show b a . Please select file Select file Q4.3 5 Points Let(). be a sequence of real numbers with a se for each n 21. ande e R such that Show that then a SC

Answer 1

Solution? Let (on ne be numbers and - an a a at sequence such of real that R 4.7 - 1. Definition of "On a ”. an number that a E for positive N EN such means for every there exist an all min lan-al <E. an = a - lim ngoo # 4.2 consider a seguience (bn) mo, given by rean bna do 24 r. if n < 2020 an if n7, 2020 Since for any 2020 br behaves like an. but an a - » for every Jan-a) such that ero <e FoNEN F nyn. for no. since of bna 24 so we only choose finite N7 2020 n

مو =طره - حصهطتووم » Also an a lim an za 1 an = a - 1 lim no - » lim bn = a no { an abn when no - Hence bna # 4.3 let enns of real no. each nyl with and be a an sin e GIR such - Cnc seguenue for that Since taking an san lin both side . an a و یک هد Hence proved.