Problems:

```
  1) I want to remove the pesky grid lines from the bar plot.

  2) I want a separate bar plot some distance from the others with the labels n and n+1.        
     Similar to picture 1 below.

  3) I would like to shade the entire area above the curve of 1/x and underneath the bars.
     in a different colour. As well as sketch a line along the edge of 
     those bars, that will be above that of 1/x but converging towards it.  

  4) I also want to be able to shade the area between two points, underneath the graph of       
     1/x (2-4 for example) to depict the partial sums.

```

I have tried rigorously to do the first three of these problems to no avail, any help would be much appreciated, thank you!

Firstly, here is my code:

```
\begin{tikzpicture}
\begin{axis}[
        grid=none,
        axis lines=left,
        major tick length=0,
        ymajorgrids=false,
        xmajorgrids=false,
        xmin=0,
        xmax=10,
        ymin=0,
        ymax=1.1,
        ybar interval=1,
        xticklabel style={/tikz/xshift=10pt},
        xtick={1,2,3,4,5,9},
        xticklabels={1,2,3,4,5,n},
        ytick=1,
        yticklabel=1,
]
\addplot[
    fill=gray!60,
]
    coordinates{
    (1,1)
    (2,1/2)
    (3,1/3)
    (4,1/4)
    (5,1/5)
    (6,1/6)
    (7,1/7)
};  
    coordinates{
    (9,1/9};    
\addplot[
    domain=0:10,
    smooth,
    samples=100,
    color=blue,
    line width=0.5mm,
]
{1/x};  
\end{axis}      
\end{tikzpicture} \\

```

What I would like to achieve is something like this: [![Harmonic series and 1/x](https://i.stack.imgur.com/FRgAd.png)](https://i.stack.imgur.com/FRgAd.png)

What I currently have is this:

[![area between harmonic series and 1/x](https://i.stack.imgur.com/fCUQc.png)](https://i.stack.imgur.com/fCUQc.png)