Determine whether the sequence {an}inftyn=2 with an =frac{ln}{n}n2converges. Show all steps.

Harlen Pritchard 2020-11-24 Answered

Determine whether the sequence {an}
n=2 with an=lnnn2 converges.

Show all steps.

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Expert Answer

Dora
Answered 2020-11-25 Author has 98 answers

Let us consider

f(x)=lnxx

where

xR and an=lnnn

for natural number

n2.

Now

We limnan=limxf(x)

Therefore, using L'hospital we can say that

limnan=limn×lnnn=limn1nlimn1=0

limf(x)=lim(lnx)1

Hence limx×lnxx=0

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