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How would you explain this (inequalities/logarithms)

Why is 1n+1<ln(n+1n\frac{1}{n+1} < ln(\frac{n+1}{n}

I got to the RHS through a simple integral, but I'm stumped on how to show this
Original post by TheFOMaster
Why is 1n+1<ln(n+1n)\frac{1}{n+1} < ln(\frac{n+1}{n})

I got to the RHS through a simple integral, but I'm stumped on how to show this


Consider geometrically the area under f(x)=1xf(x)=\frac{1}{x} between n,n+1n, n+1 and compare it to the appropriate area represented by 1n+1\frac{1}{n+1}

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