馬克勞林級數 求此函數的f(x)=x^3cos(2x)馬克勞林級數 急!! 感謝QAQ?

cos 2x
= 1 - (2x)^2/2! + (2x)^4/4! - ..... + (-1)^n*(2x)^(2n)/(2n)! + .....
= 1 - 2^2*x^2/2! + 2^4*x^4/4! - ..... + (-1)^n*2^(2n)*x^(2n)/(2n)! + .....
收斂區間為｜2x｜< ∞ , 即｜x｜< ∞

x^3 * cos 2x
= x^3 * [ 1 - 2^2*x^2/2! + 2^4*x^4/4! - ..... + (-1)^n*2^(2n)*x^(2n)/(2n)! + ..... ]
= x^3 - 2^2*x^5/2! + 2^4*x^7/4! - ..... + (-1)^n*2^(2n)*x^(2n+3)/(2n)! + .....

Ans:
f(x) = x^3 - 2^2*x^5/2! + 2^4*x^7/4! - ..... + (-1)^n*2^(2n)*x^(2n+3)/(2n)! + .....
收斂區間為｜x｜< ∞