Do you Cesaro mean? You can use the results about that taking the logarithm.
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:
Since
Therefore
Thus
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