Trying to write a script that solves a series

The series goes 1-1/3!+1/5!-1/7!+.....20 terms

This is my first guess on how to solve it. Don't have software available to me at the moment. This is a start but I have a feeling something isn't right here.

a0=1/factorial(0); %first term
an=1/factorial(38); %final term
n=0; Initialize
sumf=0; %initialize sum of series
sign=1; %initialize sign
for tn=a0: -1 / factorial(n+2):an ; %step size negative due to decreasing values.
  sumf = (sumf + tn) . * sign;
  sign= (sign .* -1); %update sign
  n=n+2; %The n is update within the factorial increment
end

any problems with this? can you update an increment?

[EDITED, Jan, code formatted]

Answer 1

[José-Luis]

A few problems, mostly regarding numerics

1. A factorial can only be represented accurately in double precision up to 21. Same applies for the inverse
2. Your different terms will span many orders of magnitude. Adding terms like that kills accuracy.

If you want accurate results and have the symbolic math toolbox you could look into vpa().

[steve guy]

Hi Jose. I'm not concerned with the accuracy just that the code itself. If I assign an increment value of -1/factorial(2) is that really just a redundant way of saying -1/2?