What's this?
- When studying math, I saw the above phrase.
- I think the meaning of its phrase is unclear, so I searched for it.
What I learned
What's series in math?
- There are many expressions for series, but here, I'll post the definition of MIT's Introduction to Numerical Analysis course material.
A sequence is a possibly infinite collection of numbers lined up in some order:
A series is a possibly infinite sum:
That is, a series is a "sum" of a sequence.
What's "sum of the series"?
The problem is what "sum" of the series means.
This expression can be interpreted in two ways; to evaluate the series, and to summarize multiple series in some way.
(something like this??)
I couldn't find any information resource that writes the definition. But when solving some math problems, I came to think the answer responded below is one of the definitions.
A series is the sum of a sequence. This is usually presented as an unevaluated summation of the terms of the series.
While the value of the series would be the pedantically correct parlance, the sum of the series is used to indicate evaluating that summation.
In conclusion at this time, we mean an unevaluated summation when saying "series", while we calculate the value of the series when saying "sum of the series".
