Inequality with logarithms How do I show that 1 n &#x2212;<!-- - -->

Landon Bonilla

Landon Bonilla

Answered question

2022-05-23

Inequality with logarithms
How do I show that
1 n 1 ln ( n n 1 )
for n>1?
As far as I can tell, exponentiating both sides with base e won't help, because then I get a nasty term on the LHS.

Answer & Explanation

elladanzaez

elladanzaez

Beginner2022-05-24Added 8 answers

We know that for any t 0
log ( 1 + t ) tsince when t 0
0 t 1 1 + x d x 0 t d x
Then take t = x 1 Note equality is true t = 0
infogus88

infogus88

Beginner2022-05-25Added 1 answers

For n > 1 we have ln ( n n 1 ) = ln ( n ) ln ( n 1 ) = n 1 n 1 x d x 1 n 1

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