This doesn't arise for singly-infinite sequences, as these have only finite sums.

Such a series can be identified with a finite sum, so it is only infinite in a trivial sense.

This means that we can form finite direct sums and direct products.

"They have to raise funds, but at least it's raising a finite sum."

More generally, one can consider finite direct sums of matrix algebras.

A finite direct sum of fields is a semi-local ring.

In this generalisation, the finite sum is replaced by an infinite series.

The general case may be expressed as a finite sum:

The finite sums of money available are likely to mean that not everyone can be compensated.

With the norm in place, absolutely convergent series can be used instead of finite sums.