Am i doing right for these two question

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thanks.
 

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That a_n-->0 in \sum a_n 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
\Sigma a_n
converge, not a sufficient condition!

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

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