I have seen other posts related to this issue, but I haven't been able to vertically center the last column of my table:
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage[table]{xcolor}
\newcolumntype{L}{>{$}l<{$}}
\newcolumntype{M}[1]{>{\raggedright\arraybackslash$}m{#1}<{$}}
%_________________________________
\begin{document}
\rowcolors{1}{gray!5}{gray!15}
\begin{tabular}{M{1cm} M{1cm} M{1cm}}
a&b&c\\[14pt]
u&v&w\\[14pt]
\end{tabular}
\end{document}
Apparently, (\centering)\arraybackslash
isn't the solution here.
Edit:
I don't know if this is the way to go, but I'll edit my question in response to CarLaTeX's answer. What I'm ultimately trying to do is
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage[table]{xcolor}
\newcolumntype{L}{>{$}l<{$}}
\begin{document}
\rowcolors{1}{gray!5}{gray!15}
\begin{tabular}{L L}
%
(1+x)^{\alpha}
&=1+ \alpha x+\frac{\alpha(\alpha-1)}{2!}x^{2}+\cdots+\frac{\alpha(\alpha-1)\cdots(\alpha-n+1)}{n!}x^{n}+\mathcal{O}\left(x^{n+1}\right)
\\[14pt]
%
\frac{1}{\sqrt{1+x}}
&=1-\frac{x}{2}+\frac{3}{8}x^{2}-\cdots+(-1)^{n}\frac{1\times 3\times\cdots.\times.(2n-1)}{2\times 4\times\cdot\times 2n}x^{n}+\mathcal{O}\left(x^{n+1}\right)
\\[14pt]
\end{tabular}
\end{document}
but vertically centered. Following CarLateX's suggestion regarding the minimum width of the columns,
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{matrix}
\tikzset{
mymatrix/.style = {
matrix of math nodes,
nodes={inner ysep=7pt, minimum width=4cm, text height=2ex, text depth=.75ex},
every odd row/.style={nodes={fill=gray!5}},
every even row/.style={nodes={fill=gray!15}},
row sep=-\pgflinewidth,
column sep=-\pgflinewidth,
inner sep=0pt
},
}
\begin{document}
\begin{tikzpicture}
\matrix[mymatrix]{
(1+x)^{\alpha}
&=1+ \alpha x+\frac{\alpha(\alpha-1)}{2!}x^{2}+\cdots+\frac{\alpha(\alpha-1)\cdot\ldots\cdot(\alpha-n+1)}{n!}x^{n}+\mathcal{O}\left(x^{n+1}\right)
\\
%
\frac{1}{\sqrt{1+x}}
&=1-\frac{x}{2}+\frac{3}{8}x^{2}-\ldots+(-1)^{n}\frac{1\times 3\times\ldots\times(2n-1)}{2\times 4\times\ldots\times 2n}x^{n}+\mathcal{O}\left(x^{n+1}\right)
\\ };
\end{tikzpicture}
\end{document}
I get
for example. But, of course, I don't want the 1st column to be as long as the second.
Also, how would I flush the text to the left of the nodes? Using anchor=west, well, anchors the node rather than the text.