Determine whether the sequence converges or diverges \(\displaystyle{a}_{{n}}={\frac{{{\ln{{\left({n}^{{3}}\right)}}}}}{{{2}{n}}}}\)

Polchinio3es

Polchinio3es

Answered question

2022-03-27

Determine whether the sequence converges or diverges
an=ln(n3)2n

Answer & Explanation

arrebusnaavbz

arrebusnaavbz

Beginner2022-03-28Added 18 answers

Given an=ln(n3)2n
We have to find limnan
limnan=limn3lognn=
Use l'Hospital Rule
limnan=limn3d(logn)dnd(n)dn
limnan=limn3n1=3
limnan=0
The sequence is convergent

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