- #1
kidsmoker
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Homework Statement
Find a sequence [tex]a_{n}[/tex] which is non-negative and null but where [tex]\sum (-1)^{n+1} a_{n}[/tex] is divergent.
Homework Equations
Alternating series test:
Let [tex]a_{n}[/tex] be a decreasing sequence of positive real numbers such that [tex]a_{n}\rightarrowa[/tex] as [tex]n\rightarrow\infty[/tex]. Then the series [tex]\sum (-1)^{n+1} a_{n}[/tex] converges.
The Attempt at a Solution
I'm a bit confused by this one. If [tex]a_{n}[/tex] is non-negative and null then it seems like it's decreasing to zero, in which case it satisfies the alternating series test. So how can the sum diverge?!
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