How do I graph only integers using the list function?

Question

I have plotted the following function using the following code:

integers = Table[Integer[n], {n, 20}];
ListPlot[Table[{x, 
x^(-1)*Sum[((6.674*(10^(-11))*(10^17) (4))/((100^2 - 
       400 (2 Cos[(2 Pi k)/x] - 3 Sin[(2 Pi k)/x]) + 
       29)^1.5)), {k, 0, x - 1}]}, {x, integers}]]

The function oscillated because it takes values that are not integers. I have searched around and the above does not work. I'm new to mathematica. How can I change the code to make it only use integer values of x?

Answer 1

You can useDiscretePlot:

f[x_] := Sum[((6.674*(10^(-11))*(10^17) (4))/((100^2 - 
         400 (2 Cos[(2 Pi k)/x] - 3 Sin[(2 Pi k)/x]) + 29)^1.5)), {k, 
    0, x - 1}]/x
DiscretePlot[f[n], {n, 1, 20}, PlotRange -> Full]

Answer 2

There is a lot to be said for making code easier to read. In this case we can write

data = Table[{x, x^(-1)*Sum[((6.674*(10^(-11))*(10^17) (4))/((100^2 - 
       400 (2 Cos[(2 Pi k)/x] - 3 Sin[(2 Pi k)/x]) + 
       29)^1.5)), {k, 0, x - 1}]}, {x, 20}];

ListPlot[data]
ListPlot[data, AxesOrigin->{0,25}]

Notice that we do not define integers because Table takes care of that for us. One advantage of the above is that we can examine our data with

data // Dataset

and we can add options to our ListPlot to build up the command we want. The optional arguments are added in any order after the required arguments. They always have the form of rules, like PlotRange->{All,{25,30}}

We can see the coordinates of a plotted data point by using ListPlot[Tooltip[data]] as the basic command and hovering the mouse pointer over the point whose coordinates we want.