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# Convergence of a sequence watch

1. To determine whether a sequence converges, is it ok if the ratio test is used to determine whether the series converge, if it does then it implies the sequence converges, or is this not always the case?
2. Say the sequence is . If the series converges, then it's not too hard to prove that tends to zero, and so tends to zero.

So if converges, then also converges (to zero). But the converse is not true: could converge, but may diverge. For example the trivial example clearly converges, but the corresponding sum clearly diverges.
3. (Original post by Unbounded)
Say the sequence is . If the series converges, then it's not too hard to prove that tends to zero, and so tends to zero.

So if converges, then also converges (to zero). But the converse is not true: could converge, but may diverge. For example the trivial example clearly converges, but the corresponding sum clearly diverges.
Thanks.

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Updated: April 8, 2011
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