This is a worthwhile point. The non-alternating sequence, 1/(2n + 1), when summed, diverges. So if you cut it at the 100th term, or the 1000000th term, the sum of the tail will not be negligible, it will be infinite.
It's only the fact that it's alternating that makes it summable. The alternating series converges like 1/n^2.
This is the kind of thing that, if it's noted in an interview situation, marks a better than average candidate. It could also allow such a candidate to go on about problems with summing series, and really show off. (One secret to interviewing well being to make the given question into a question you know something about already.)
It's only the fact that it's alternating that makes it summable. The alternating series converges like 1/n^2.
This is the kind of thing that, if it's noted in an interview situation, marks a better than average candidate. It could also allow such a candidate to go on about problems with summing series, and really show off. (One secret to interviewing well being to make the given question into a question you know something about already.)