The most simple way to split equations, left align them and have a space between them?

Question

I have four equations which I want to split, align and make sure there is a space between the equations.

\begin{align*} 
    \sum^\infty_{i=1} (3t_{2i-1}+t_{2i})9^{-i} \\
    =\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})3^{-2i}\\
    = \sum^\infty_{i=1} 3^{-(2i-1)} t_{2i-1} + 3^{-2i} t_{2i}\\  
    =\sum^\infty_{i=1} t_i 3^{-i}
\end{align*}

I tried using the align environment, but it aligns to the right.

I tried using flalign but this leaves no space between the equations.

Answer 1

Something like

\documentclass[preview]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{align*} 
&\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})9^{-i}&& \\
&=\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})3^{-2i}\\
&= \sum^\infty_{i=1} 3^{-(2i-1)} t_{2i-1} + 3^{-2i} t_{2i}\\  
&=\sum^\infty_{i=1} t_i 3^{-i}
\end{align*}
\end{document}

should do what you want:

You can play arround with the & signs a bit to get exactly what you want.

Answer 2

I'm not sure what you mean by not leaving space between the equations, but flalign works fine; see below. Image at the top is flalign*, at the bottom it's align*.

\documentclass[preview]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{flalign*} 
&\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})9^{-i}&\\
&=\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})3^{-2i}&\\
&= \sum^\infty_{i=1} 3^{-(2i-1)} t_{2i-1} + 3^{-2i} t_{2i}&\\  
&=\sum^\infty_{i=1} t_i 3^{-i}
\end{flalign*}
\begin{align*} 
&\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})9^{-i}\\
&=\sum^\infty_{i=1} (3t_{2i-1}+t_{2i})3^{-2i}\\
&= \sum^\infty_{i=1} 3^{-(2i-1)} t_{2i-1} + 3^{-2i} t_{2i}\\  
&=\sum^\infty_{i=1} t_i 3^{-i}
\end{align*}
\end{document}