convergence Q: prove that if An->a and An-Bn->0 then Bn->a

[transgalactic]

prove that if An->a and An-Bn->0 then Bn->a

??

 

[stapel]

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.

 

[daon]

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| <= ??