Series Convergence: Show AK -> 0 as K->∞

[hth]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I'm not really sure how to go about this proof. But, this is my attempt,

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

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

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

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

 

[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?