Question

You can tell if a sequence converges by looking at the first 1000 terms.

a. True
b. False

Answer 1

definently false, it could be conditionally convergent

Answer 2

b. False

Explanation:

A convergent sequence is a sequence that approach to a specific limit. If the sequence doesn't approach to a limit, then it's a divergent sequence.

Now, if we have a sequence apparently convergent where we just analyse the first 1000 terms, that information won't be enough to actually consider the complete sequence as convergent, because those 1000 terms are not representative of the actual limit.

Therefore, the answer is false.