Prove, using the definitio of a convergent sequence \lim_{n \rightarrow

Mlejd5

Mlejd5

Answered question

2022-01-23

Prove, using the definitio of a convergent sequence
limnln({nn+1})=0

Answer & Explanation

Jaiden Conrad

Jaiden Conrad

Beginner2022-01-24Added 14 answers

limnln({nn+1})=0
Let |ln(nn+1)|<ϵ
e|ln(nn+1)|<eϵ
nn+1<eϵ
11n+1<eϵ
1eϵ<1n+1
11eϵ>n+1
11eϵ1>n
eϵ1eϵ>n
Given, ϵ>0, choose n0=|eϵ1eϵ|
Therefore, given any ϵ>0, we can find a positive integer n0
|ln(nn+1)|<ϵ

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