Question Number 145065 by Ar Brandon last updated on 02/Jul/21
![(1/( (√(1+x))))=1+Σ_(k=1) ^n [(((−1)^k )/2^(2k) )C_(2k) ^k ]x^k +o(x^n )](Q145065.png)
$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}}}=\mathrm{1}+\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2}^{\mathrm{2k}} }\mathrm{C}_{\mathrm{2k}} ^{\mathrm{k}} \right]\mathrm{x}^{\mathrm{k}} +\mathrm{o}\left(\mathrm{x}^{\mathrm{n}} \right) \\ $$