Exercise 3 If a_(n) is a convergent a_(n)>=L for all n, then \lim_()a_(n)>=L. Similarly prove if a_(n) is a convergenta_(n)<=U for all n, then \lim_()a_(n)<=U.To gether these give a very useful way to bound a limit. if s_(n) is a convergent sequence with L<=s_(n)<=U forall n, then L<=\lim_()s_(n)<=U.Exercise 4 Let x_(n),y_(n) be two convergent sequences with the same limit. Prove directly (ie don't just use thesqueeze theorem) that the interleaved sequence s_(n) defined byx_(0),y_(0),x_(1),y_(1),x_(2),y_(2),x_(3),y_(3),dots,x_(n),y_(m)dotsalso converges, and has the same limit.