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 8 '17 at 12:10[l]
and not without it? – Daniel Martin Jul 8 '17 at 12:12[l]
? As an optional argument ofalign
? – Bernard Jul 8 '17 at 12:14\begin{align*}
with\begin[l]{align*}
. – Daniel Martin Jul 8 '17 at 12:25&
. See my other comment under berkus'answer. – Bernard Jul 8 '17 at 12:27