2

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
3

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:

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.