Determine whether the given sequence is convergent or divergent an=ln⁡(n+1)n

Natasha Henry

Natasha Henry

Answered

2022-01-25

Determine whether the given sequence is convergent or divergent
an=ln(n+1)n

Answer & Explanation

Johnny Cummings

Johnny Cummings

Expert

2022-01-26Added 7 answers

an=ln(n+1)n
Now,
limnan=limnln(n+1)n, [] form
=limn=1(n+1)12n
=limn2nn+1
=limn2nn(1+1n)
=limn2nnn(1+1n)
=2(1+1n)=0
Thus, limnln(n+1)n=0
Hence, an converhes to 0

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