Am i doing right for these two question

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SUMMARY

The discussion clarifies that the condition \( a_n \to 0 \) in the series \( \sum a_n \) does not guarantee convergence. It emphasizes the necessity of understanding that while \( \lim a_n = 0 \) is required for convergence, it is not sufficient. The comparison to the harmonic series \( \sum \frac{1}{n} \), which diverges, illustrates this point effectively.

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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.
 

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