math
posted by eng on .
how do i represent 1/(1+x^4) in general taylor polynomial. I know the pattern is 1x^4+x^8x^16..... I don't know how to represent this pattern in variables equation form. What i mean by general taylor polynomail is for example
1/(1x)=1+x+x^2+x^3...+x^n. What is need is after ....

I would write it as
(1+x^4)^1 and apply the general binomial theorem to get
= 1^1 + (1)(1^2/1!(x^4) + (1)(2)(1^3)/2! (x^4)^2 + (1)(2)(3)(1^3)/3! (x^4)^3 + ...
= 1  x^4 + x^8  x^12 + x^16  x^20 + ...
for 1 < x < +1
I tested for x = .25 and my margin of error was 4.17x10^10 using the above 6 terms