Prove the if the series converges then the collection additionally converges. Also, give an example to display that the converse is false, i.e., a instance in i m sorry converges however does not.
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Proof. i think converges. Then we recognize
The first sum is a finite amount so that converges, and also the 2nd sum converges through comparison through . Hence, converges
Counterexample. The converse is false. Let
Prove the if ∑ an converges climate ∑ (an)1/2 n-p converges because that p > 1/2
Prove the ∑ 1/an diverges if ∑ an converges
Point the end an error, questioning a question, offer an different solution (to use Latex form
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