Asked by eng
how do i represent 1/(1+x^4) in general taylor polynomial. I know the pattern is 1-x^4+x^8-x^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/(1-x)=1+x+x^2+x^3...+x^n. What is need is after ....
1/(1-x)=1+x+x^2+x^3...+x^n. What is need is after ....
Answers
Answered by
Reiny
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
(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
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