Answer to Question #234342 in Calculus for Sha

Question

How to solve binomial expansion of (2+x)^(-1/2)

Answer 1

$\text{By binomial expansion we know that}\\ (x+y)^r = \sum^\infty_{k=0}\begin{pmatrix} r\\k\end{pmatrix}x^{r-k}y^k\\ \therefore (2+x)^{-\frac{1}{2}} = 2^{-\frac{1}{2}}-\frac{1}{2}.2^{-\frac{3}{2}}x+\frac{3}{8}.2^{-\frac{5}{2}}x^2$