# Series convergence

1. Dec 1, 2009

### hth

1. The problem statement, all variables and given/known data

Show that if $$\sum$$ak converges, then $$\sum$$ from k to ∞ of ak goes to zero as k goes to ∞.

2. Relevant equations

3. The attempt at a solution

First I tried to show that $$\sum$$ak is convergent.

Let c be a real number and ε > 0. So there is an integer N > 0 such that if n > N then |an - c | < ε.

So c is the limit of the sequence and an -> c.

I don't really know where to go from there. Any help is appreciated.

2. Dec 1, 2009

### Dick

The definition of convergence of a series uses partial sums. What's the sum from k to infinity in terms of a partial sum?