How to prove the convergence of the series &#x2211;<!-- ∑ --> ( 3 n

Hailie Blevins

Hailie Blevins

Answered question

2022-06-24

How to prove the convergence of the series ( 3 n + 2 ) n 3 n 2 n

Answer & Explanation

Lamont Adkins

Lamont Adkins

Beginner2022-06-25Added 11 answers

The root test applies nicely here. Taking a n = ( 3 n + 2 n 2 ) n gives
lim n | a n | 1 / n = lim n 3 n + 2 n 2 = 0 < 1
This proves that a n converges so your series 1 3 a n converges.

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