How to solve binomial expansion of (2+x)^(-1/2)
By binomial expansion we know that(x+y)r=∑k=0∞(rk)xr−kyk∴(2+x)−12=2−12−12.2−32x+38.2−52x2\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^2By binomial expansion we know that(x+y)r=∑k=0∞(rk)xr−kyk∴(2+x)−21=2−21−21.2−23x+83.2−25x2
