2015/033) Find coefficient of $x^n$ in the expansion of $\sqrt{1 + 2x + 3x² + 4x³ +\cdots inf. }$

let $y = ( 1 + 2x + 3x^2 + 4x^3 + \cdots. inf.) \cdots(1)$
y converges for |x| < 1
now $xy = x + 2x^2 + 3x^3 \cdots(2)$
subtract (2) from (1)
$y - xy = 1 + x + x^2\cdots = \dfrac{1}{1-x}$
so $y(1-x) = \dfrac{1}{1-x}$
or $y = \dfrac{1}{(1-x)^2}$
so $\sqrt{1 + 2x + 3x² + 4x³ +\cdots inf. }=\dfrac{1}{1-x} = 1 + x + x^2\cdots$.
so coefficient of $x^n$  1 for all n