# LaTex error- !Paragraph ended before \split was complete

I am using amsmath package but keep getting errors with the following:

\begin{split}
$A_R&=\frac{4}{9}+\frac{20}{81}+\frac{100}{729}+\frac{500}{6561}+\dots \\ &=\frac{4}{3^2}+5\times\frac{4}{3^4}+5\times5\times\frac{4}{3^6}+5\times5\times5\times\frac{4}{3^8}+\dots \\ &=\sum_{n=1}^{\infty}5^{n-1}\times\frac{4}{3^{2n}} \\ &=\sum_{n=0}^{\infty}5^{n-1}\times\frac{4}{3^2n+2}} \\ &=\frac{\frac{4}{9}}{1-\frac{5}{9}} \\ &=1$
\end{split}


The error is detected on the line after \end{split} and I cannot understand why. I also get:

! Argument of \split has an extra }.
! Extra }, or forgotten \endgroup.

• Wrong nesting order and spurious closing brace at the end of line 4. It should be $\begin{split} A_R&=\frac{4}{9}+\frac{20}{81}+\frac{100}{729}+\frac{500}{6561}+\dots \\ &=\frac{4}{3^2}+5\times\frac{4}{3^4}+5\times5\times\frac{4}{3^6}+5\times5\times5\times\frac{4}{3^8}+\dots \\ &=\sum_{n=1}^{\infty}5^{n-1}\times\frac{4}{3^{2n}} \\ &=\sum_{n=0}^{\infty}5^{n-1}\times\frac{4}{3^2n+2} \\ &=\frac{\frac{4}{9}}{1-\frac{5}{9}} \\ &=1 \end{split}$ – Gonzalo Medina Feb 4 '15 at 17:46
• Why don't you use align* instead? – Gonzalo Medina Feb 4 '15 at 17:47
• Thank you! I have used yours and changed split to aligned and it is now working :) Thank you very much!! – Rachel Feb 4 '15 at 18:07

The very last } of the line &=\sum_{n=0}^{\infty}5^{n-1}\times\frac{4}{3^2n+2}} \\ shouldn't be there. Plus, the split environment must be placed inside math mode, not outside:
$\begin{split} A_R&=\frac{4}{9}+\frac{20}{81}+\frac{100}{729}+\frac{500}{6561}+\dots \\ &=\frac{4}{3^2}+5\times\frac{4}{3^4}+5\times5\times\frac{4}{3^6}+5\times5\times5\times\frac{4}{3^8}+\dots \\ &=\sum_{n=1}^{\infty}5^{n-1}\times\frac{4}{3^{2n}} \\ &=\sum_{n=0}^{\infty}5^{n-1}\times\frac{4}{3^2n+2}} \\ &=\frac{\frac{4}{9}}{1-\frac{5}{9}} \\ &=1 \end{split}$