Finding local extrema using partial derivatives

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okevino
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see attachment
thanks.
 

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That a_n-->0 in [tex]\sum a_n[/tex] does not imply that the series is convergent. You should re-read that theorem in your notes/book more carefully to see what it's actually saying.
 
lim an= 0 is a necessary condition that
[tex]\Sigma a_n[/tex]
converge, not a sufficient condition!

The first one "compares" to the sum of 1/n which does NOT converge.