Alternating series test

  • Thread starter georg gill
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Alternating series test:

1. All the [tex]u_n[/tex] are all positive

2. [tex]u_n\geq u_{n+1}[/tex] for all [tex]n \geq N[/tex]. For some integer N

3. [tex]u_n \rightarrow 0[/tex]


I thought it would hold with 2. and that the su m of the N first terms were not [tex]\infty[/tex]

Here is the theroem just in case:

http://bildr.no/view/1047382

Here they assume N=1 how can they do that?
 

Answers and Replies

  • #2
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Alternating series test:

1. All the [tex]u_n[/tex] are all positive

2. [tex]u_n\geq u_{n+1}[/tex] for all [tex]n \geq N[/tex]. For some integer N

3. [tex]u_n \rightarrow 0[/tex]


I thought it would hold with 2. and that the su m of the N first terms were not [tex]\infty[/tex]
How can the sum of the first N terms ever equal infinity?? If you add up finitely many real number, then you never get infinity.

Here is the theroem just in case:

http://bildr.no/view/1047382

Here they assume N=1 how can they do that?
The proof for arbitrary N is very similar. Try to prove it yourself!!
(or even better: reduce to the case N=1)
 

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