T transgalactic Junior Member Joined Nov 20, 2008 Messages 58 Dec 4, 2008 #1 prove that if An->a and An-Bn->0 then Bn->a ??

stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 15,948 Dec 4, 2008 #2 You've had plenty of these sorts of exercises set up or even completed for you recently, so of course you now have a solid understanding of the topic and techniques. What have you tried so far? Where are you stuck? Please be complete. Thank you! Eliz.

You've had plenty of these sorts of exercises set up or even completed for you recently, so of course you now have a solid understanding of the topic and techniques. What have you tried so far? Where are you stuck? Please be complete. Thank you! Eliz.

D daon Senior Member Joined Jan 27, 2006 Messages 1,284 Dec 4, 2008 #3 epsilon > 0. Let N1 be chosen so that n>N1 implies |An-a|<epsilon/3. Let N2 be chosen so that n>N2 implies |An-Bn|<epsilon/3. Let N = max{N1,N2} Then let n > N. |Bn-a| = |Bn - a - An + An| <= ??

epsilon > 0. Let N1 be chosen so that n>N1 implies |An-a|<epsilon/3. Let N2 be chosen so that n>N2 implies |An-Bn|<epsilon/3. Let N = max{N1,N2} Then let n > N. |Bn-a| = |Bn - a - An + An| <= ??