Evaluate an Infinite Series in Closed Form

[avocadogirl]

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.

 

[quantumdude]

"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.

 

[avocadogirl]

Thank You!