Prove/disprove convergence of two series.

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

Re: Prove/disprove convergence of two series.

Do you Cesaro mean? You can use the results about that taking the logarithm.

Re: Prove/disprove convergence of two series.

Quote:

Originally Posted by

**girdav** Do you Cesaro mean? You can use the results about that taking the logarithm.

Figures. Reading that, it sounds like it's *exactly* what I need, but we *skipped* the section that describes it. Thanks for your help!