creating a function in different function

Hello guysi

I need to prepare a function the term numbers increase, when the new value becomes 1/1000 of the total value, the term increase will end. but I have to define this as a function because the equations I will write as a combination function will be replaced by increasing the power of x in the g(x). like that;

f(x)=1-(x^2/2^1)+(x^4/2^2)-(x^6/2^3)....+(x^12/2^6)...... (when new term is 1/1000 of f(x) for x value stop the function)

after stopped f(x) for example = f(x)=1-(x^2/2^1)+(x^4/2^2)-(x^6/2^3)

(I need move on to new function)

g(x)=f(x) + f(x^2)/(2^2) + f(x^3)/(2^3) + f(x^4)/(2^4)...... (when new term is 1/1000 of g(x) for x value stop the function)

thank you guys