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does an alternating series converge

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Under what conditions does an alternating series converge?
An alternating series 
an
n = 1
 = 
(−1)n − 1bn,
n = 1
 where bn = |an|,
 converges if 
0 < bn + 1 ≤ bn
 for all n, and 
lim n → ∞ 

bn =

Apr 24th, 2015

For any convergent series S(a_n) must be lim(a_n) = 0 (and therefore lim(|a_n|) = 0).

So here lim(b_n) = 0.

Apr 24th, 2015

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Apr 24th, 2015
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Apr 24th, 2015
Sep 25th, 2017
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