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Question Number 209232 by alcohol last updated on 04/Jul/24
u0=a,un+1=unvnv0=b∈]0,1[,vn+1=12(un+vn)∙showthata⩽un⩽un+1⩽vn⩽vn+1⩽b∙showthatvn−un⩽a+b2n
Answered by Berbere last updated on 04/Jul/24
u0=a⩾0ifa<0U1Willnotdefinedv0=b>awewillshowun>0andvn>0....P(n)u0=a>0&v0=b>0p(n+1)..{un+1unvn>0;vn+1=12(un+vn)>0}a=810;b=910u1⩽?v1⇒8.9100⩽12(1710)=517⇒8<72⩽5017<3false!tchekQuationsir!
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