Okay, this problem has been kicking my butt for several hours now.
Consider the positive sequences and with
Prove or disprove: If converges to , then
converges to .
I attempted to prove this as follows:
Did I even remotely do that right? I feel like I should be using the
triangle inequality to prove this, but I haven't been able to produce
a useful result with it. The best I have is:
I could probably get a more useful result if , but I can't find a single effective way to prove that