Evaluate an Infinite Series in Closed Form

1. Feb 28, 2009

My question is one of vocabulary. What does it mean to evaluate an infinite series in closed form?

If I have a Series: $$\Sigma$$ 1/ (N2), as N goes from 1 to infinity.

This is similar to a test question I'm working on so, I DO NOT want to know how to solve it, I just want to know exactly what is meant by evaluating an infinite series in closed form.

2. Feb 28, 2009

Tom Mattson

Staff Emeritus
"Expressed in closed form" means "expressed as sum of finitely many well-understood functions".

Here's an example. Let $|x|<1$. Then,

$$\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}$$

The expression on the left hand side is an infinite series, but the expression on the right is in closed form.

3. Feb 28, 2009