Hi. Here is a slight addition that you can play with if you wish.
I just modified this portion so we can watch the convergence.
I also eliminated multiplying the answer by 100.
Just format the output as percentage to 3 decimal places does the same
thing!

For J = 2 To 20
.Add "k", Y / Fx.Fact(J) ' T/j!
.Add "M", [MMult(M, Orig)] 'Matrix to the next power

.Add "Old", [Ans]
.Add "Ans", [Ans + k*M] 'Sum
Debug.Print J; Fx.SumXMY2([Old], [Ans])
Next J
[A12].Resize(9, 9) = [Ans]
End With
End Sub

The output is:
2 0.03359136055325
3 9.2432006386492E-04
4 1.54269946074966E-05
5 1.72307843099531E-07
6 1.35605071782519E-09
7 7.91983983820038E-12
8 3.54955567034313E-14
9 1.25992350330859E-16
10 3.62323283207642E-19
11 8.61641664106313E-22
12 1.72167126878345E-24
13 2.93590834028579E-27
14 4.50356058499773E-30
15 1.36904585529777E-32
16 4.48415508583941E-44
17 0
18 0
19 0
20 0

We can see that around 8-9 loops is all that's needed.
One can modify the code to exit once the difference gets below a certain
level.

= = = = =
HTH
Dana DeLouis

snip