Show that the sequence is non decreasing. 
I was doing $$x_{n+1}-x_n= \frac {1}{n+1}-\ln \left(1+\frac{1}{n+1}\right)$$
but now how to proceed further and how to use this diagram?

The sum of the areas of the rectangles from $x=1$ up to $x=n+1$ is $\sum_{k=1}^n1/k$ and the area under the curve $y=1/x$ from $x=1$ up to $x=n+1$ is $\int_{1}^{n+1}\frac{dx}{x}=\ln(n+1).$ Now just compare the two
