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Question Number 139286 by qaz last updated on 25/Apr/21
$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}} }=\left(\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\right)+\left(\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\right){x}+\left(\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\right){x}^{\mathrm{2}} +\left(\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\right){x}^{\mathrm{3}} +... \\ $$
Commented by mr W last updated on 25/Apr/21
$${wrong}! \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}} } \\ $$$$=\begin{pmatrix}{{n}−\mathrm{1}}\\{\mathrm{0}}\end{pmatrix}+\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\:{x}+\begin{pmatrix}{{n}+\mathrm{1}}\\{\mathrm{2}}\end{pmatrix}\:{x}^{\mathrm{2}} +\begin{pmatrix}{{n}+\mathrm{2}}\\{\mathrm{3}}\end{pmatrix}\:{x}^{\mathrm{3}} +... \\ $$