1. Jan 26, 2014

### 939

A limit of a sequence is definetely convergent if:

If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N

My only question is what exactly are K, N, an and n? What values are they? How would they be graphed? I.e. for the sequence a(n) = 2n

n = 2
an = 4
What are K and N? Are they on the horizontal or vertical axis?

2. Jan 26, 2014

### tiny-tim

hi 939!
nooo, you mean definitely divergent

essentially, it means that the sequence converges to ∞, or to -∞

we can't use δ and ε for ∞ (because we can't get close enough to ∞ !)

so instead of small circles round the limit, we draw large circles round the limit (∞), ie x > K (or x < -K), and we say that that large circle has to contain all an once n is large enough

it's the same as saying that the sequence {1/an} has the limit 0 (from above, for the ∞ case) (or from below, for the -∞ case)​