the n-th term test for the series <munderover> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAto

Arraryeldergox2

Arraryeldergox2

Answered question

2022-06-23

the n-th term test for the series n = 1 1 / n implies that the series converges since lim n 1 / n = 0
but the series actually diverges. what is the error in the procedure followed?

Answer & Explanation

hildiadau0o

hildiadau0o

Beginner2022-06-24Added 21 answers

Be careful: the theorem states
If a n converges, then lim n a n = 0
which conversely means
If lim n a n 0 then a n does not converge.
This means that lim n a n = 0 is a necessary but not sufficient condition for a series to converge.

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