H2 maths calculus

2 (a) Show , by differentiating the series expnasion of that = 1- 2x + 3x3 - 4x'+ ... 1+x ( 1 + x ) - (b) By considering the expansion of evaluate the nth derivative of 1 when x = 0. (1 -x?)2 (1- x' )? (c) By writing (1 + x) as - {1 + (1 + 2 x)}, or otherwise, show that the coefficient of x " in the expansion N of ( 1 + x ) " (where n E Z) in ascending powers of x is (-1) " (2 n + 1). (1+ 2x)'