F.4 M1 Maths Question

2.a) Expand e^(-x/3) in ascending powers of x as far as the term in x^2

b) It is known that (1-ax)^n / e^(x/3)= 1 - 11/6x +(47/36)x^2 + ..., where a is a constant and n is a positive integer. Find the values of a and n.

Answer b) a =0.5 n=3


3.a)Expand e^(-2x) in ascending powers of x as far as the term in x^3

b)Hence, or otherwise, find the coefficient of x in the expansion of (1- 1/x + 1/x^2)e^(-2x)


4 a) Expand 1/e^(3x) in ascending powers of x as far as the term in x^2

b) the coefficient of x in the expansion of (1+x/2)^n/e^(3x) is -1/2, where n is an integer greater than 2.Find the coefficient of x^2

Answer b)-0.5

Please help urgent thxxx!!!