急! 中四數學thx :D

e^x = 1 + x + x^2/2! + x^3/3! + ...
(1) e^3x - 2e^2x
= [1 + 3x + (3x)^2/2! + (3x)^3/3! + ...] - 2[1 + 2x + (2x)^2/2! + (2x)^3/3! + ...]
= 1 + 3x + (9/2)x^2 + (9/2)x^3 + ... - 2 - 4x - 4x^2 - (8/3)x^3 - ...
= -1 - x + (1/2)x^2 + (11/6)x^3 + ...
(2) (1 + x + x^2) / (e^2x)
= (1 + x + x^2)[e^(-2x)]
= (1 + x + x^2)[1 - 2x + 2x^2 - (4/3)x^3...]
= 1 - 2x + 2x^2 - (4/3)x^3 ... + x - 2x^2 + 2x^3... + x^2 - 2x^3...
= 1 - x + x^2 - (4/3)x^3