12.2 due April 4

So the homework was pretty confusing and I've concluded that maybe I just didn't understand the last section...but here's a shout out to section 12.2...

From my observation, the proof strategy is essentially to take a summation and try to reduce it down to a limit, and then prove it the same as we did in section 12.1. I get how we choose the N and I understand how it works for n > N...I guess I just don't understand what the point of solving for epsilon (sorry, I'm not going to go on a greek letter hunt) is. Maybe I don't understand what E is at all. However, if we can prove the limit of the sequence, we can say that thus we have proved the summation as well.

I'm now going to use my words to try to understand what epsilon is. So. We are trying to prove a limit. If we can show that for some arbitrary integer less than 0, a sequence will equal a certain result less than epsilon, then we have shown that the sequence approaches a certain number. (...?) I guess that makes sense. So then we use the value we chose for N to solve for n and show that the sequence is less than epsilon for that sequence. I really hope that's right.

Now back to section 12.2. I am pretty fascinated that you can turn an infinite series problem into a limit/sequence problem. Are we just supposed to write out the first few elements of the sum and then make an estimation of what the nth term in the set would be, and then take the limit and solve?

I will most likely be taking a trip to office hours with your friend tomorrow.