How do you find the Limit of ln(n+1)-ln(n) as n approaches infinity?

Maribel Ali

Maribel Ali

Answered question

2023-03-06

How to find the Limit of ln ( n + 1 ) - ln ( n ) as n approaches infinity?

Answer & Explanation

cerisewi2

cerisewi2

Beginner2023-03-07Added 1 answers

Use ln a - ln b = ln ( a b ) and continuity of ln.
lim n 00 ( ln ( n + 1 ) - ln ( n ) = lim n ln ( n + 1 n )
= ln ( lim n n + 1 n )
= ln ( 1 ) = 0
Note that
lim n n + 1 n = lim n n ( 1 + 1 n ) n 1
= 1 + 0 1 = 1

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