# How do I plot various values of the partial sums for a function with 2 variables?

This is what I have tried so far.

I have a function defined as the below:

Multifactorial[n_, k_] := Abs[Apply[Times, Range[-n, -1, k]]]
s[i_] := Sum[1/Multifactorial[n, 1], {n, 1, i}]
ListPlot[Table[{i, s[i]}, {i, 1, 100}]]

Which results in the following plot of the partial sums of Multifactorial[n,1] .

I managed to display the partial sums when its just a single variable function (i.e. me manually inputting the argument for k).

However what I am trying to achieve is display as one plot (with different colours and a legend) the partial sums of MultiFactorial[n,1] through to MultiFactorial[n,10]. I was not able to define this as I don't know the syntax well enough.

Thanks for any and all help.