Do alternating SEQUENCES converge or diverge? I have a sequence that alternates between 0.007 and -0.007. The numbers keep decreasing, but the values are always between positive and negative values.

Question

amistre64 · Answer

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amistre64 · Answer

they can converge; conditionally or absolutely

amistre64 · Answer

they can also diverge ...

anonymous · Answer

Oooh
So, my values are between positive and negative decimals. Should I use the absolutue value test or something?

amistre64 · Answer

i would :)

anonymous · Answer

Thank you!!

amistre64 · Answer

youre welcome, and if you need a refresher on it: http://tutorial.math.lamar.edu/Classes/CalcII/AbsoluteConvergence.aspx that should help

anonymous · Answer

$$(–1)^(n + 1)\div(2n – 5)$$   This is my alternating series and sequence. My answer is that the sequence DIVERGES and the series CONVERGES.

phi · Answer

if this is $$ \frac{-1^{(n+1)}}{2n-5} $$ then its limit is 0, so the sequence also converges. See thm 2 in Paul's notes http://tutorial.math.lamar.edu/Classes/CalcII/Sequences.aspx

anonymous · Answer

$$(-1)^{n}n ^{2}\div(n(n+1))$$   My answer is that the sequence and series both diverge.

But taking the limit of the sequence gives me "1".