You may place your equations in an array environment with left alignment:
\documentclass[11pt]{amsart}
\begin{document}
And then the first several terms of $v$ are
\[
\begin{array}{l}
v_0, \\
\lambda v_0 + B, \\
\lambda^2 v_0 + 2 \lambda B + \lambda A, \\
\lambda^3 v_0 + 3 \lambda^2 B + 3 \lambda^2 A, \\
\lambda^4 v_0 + 4 \lambda^3 B + 6 \lambda^3 A, \\
\lambda^5 v_0 + 5 \lambda^4 B + 10 \lambda^4 A, \\
\end{array}
\]
\end{document}
Edit No 1:
Or you can use an align* environment, with alignment markers at the beginning of each line:
\documentclass[11pt]{amsart}
\begin{document}
And then the first several terms of $v$ are
\begin{align*}
& v_0, \\
&\lambda v_0 + B, \\
&\lambda^2 v_0 + 2 \lambda B + \lambda A, \\
&\lambda^3 v_0 + 3 \lambda^2 B + 3 \lambda^2 A, \\
&\lambda^4 v_0 + 4 \lambda^3 B + 6 \lambda^3 A, \\
&\lambda^5 v_0 + 5 \lambda^4 B + 10 \lambda^4 A, \\
\end{align*}
\end{document}

Edit No 2:
The equations are aligned at &. To demonstrate:
\documentclass[11pt]{amsart}
\begin{document}
And then the first several terms of $v$ are
\begin{align*}
&v_0, & \textrm{Aligns here}\\
&{\lambda v_0 + B}, & \textrm{Aligns here}\\
&{\lambda^2 v_0 + 2 \lambda B + \lambda A}, & \text{Aligns}\\
&{\lambda^3 v_0 + 3 \lambda^2 B + 3 \lambda^2 A}, & \text{Aligns here long}\\
&{\lambda^4 v_0 + 4 \lambda^3 B + 6 \lambda^3 A}, & \text{Ali}\\
&{\lambda^5 v_0 + 5 \lambda^4 B + 10 \lambda^4 A},& \text{Aligns here very long}
\end{align*}
\end{document}

Edit No 3:
& here has two purposes: setup the columns and setup the point where the equations will all be aligned. To demonstrate it, we should use equations with = sign, which are actually align is mainly used for. (see here) :
\documentclass[11pt]{amsart}
\begin{document}
And then the first several terms of $v$ are
\begin{align*}
x&=y & w&=z & a&=b+c\\
2x&=-y & 3w&=\frac{1}{2}z & a&=b\\
-4 + 5x&=2+y & w+2&=-1+w & ab&=cb
\end{align*}
\end{document}
1st, 3rd and 5th & determines the location of =, and the others determine the number of columns. This is how align environment is setup.

&, so all your lines are considered to be on the left side of the alignment (hence right-aligned), and there's an implicit&at the end of each line. Simply put one at the beginning of each line. – Bernard Jul 08 '17 at 12:10[l]and not without it? – Daniel Martin Jul 08 '17 at 12:12[l]? As an optional argument ofalign? – Bernard Jul 08 '17 at 12:14\begin{align*}with\begin[l]{align*}. – Daniel Martin Jul 08 '17 at 12:25&. See my other comment under berkus'answer. – Bernard Jul 08 '17 at 12:27$s, the whole paragraph inside a{quote}env, and there I didn't want terms split by line breaks. When I changed my mind to one term per row, I didn't undo the extra braces. – Daniel Martin Jul 08 '17 at 13:37