Finding local extrema using partial derivatives

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okevino
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see attachment
thanks.
 
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  • Handwritten-style series work: left side sums 2n^2+3n over 5n^3+2n+1 from n=1 to infinity, with a comparison to 2n^2/5n^3 and a limit of 2/(5n) shown as 0, concluding convergent; right side sums ln(n)/n^2 from n=2 to infinity, with a note 'hos 1/x over 2n', 0, and convergent.
    convergence2.JPG
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Discussion

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.
 

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