Khi biên dịch Latex với code dạng
\[\begin{align*} .\end{align*}\]
mình thường gặp lỗi sau. Xin mọi người hướng dẫn cách khắc phục
! Package amsmath Error: Erroneous nesting of equation structures;
(amsmath) trying to recover with `aligned'.
See the amsmath package documentation for explanation.
Type H <return> for immediate help.
...
l.9 ...frac{(1+z)^{n+1} - 1}{(n+1)z}. \end{align*}
\]
?
với code ( hoặc các dạng tương tự với câu lệnh Latex như trên )
\[ \begin{align*} S(n,z) = \sum_{k=0}^n \frac{z^k}{k+1}\binom{n}{k} &= \sum_{k=0}^n \frac{n!}{(k+1)!(n-k)!} z^k \\ &= \frac{1}{n+1} \sum_{k=0}^n \frac{(n+1)!}{(k+1)!(n-k)!} z^k \\ &= \frac{1}{(n+1)z} \sum_{k=0}^n \binom{n+1}{k+1} z^{k+1} \\ &= \frac{1}{(n+1)z} \sum_{k=1}^{n+1} \binom{n+1}{k} z^k \\ &= \frac{1}{(n+1)z} \left( -1 + \sum_{k=0}^{n+1} \binom{n+1}{k} z^k \right) \\ &= \frac{(1+z)^{n+1} - 1}{(n+1)z}. \end{align*} \]
Khi hiện thị trên diễn dàn thì hoàn toàn bình thường
\[ \begin{align*} S(n,z) = \sum_{k=0}^n \frac{z^k}{k+1}\binom{n}{k} &= \sum_{k=0}^n \frac{n!}{(k+1)!(n-k)!} z^k \\ &= \frac{1}{n+1} \sum_{k=0}^n \frac{(n+1)!}{(k+1)!(n-k)!} z^k \\ &= \frac{1}{(n+1)z} \sum_{k=0}^n \binom{n+1}{k+1} z^{k+1} \\ &= \frac{1}{(n+1)z} \sum_{k=1}^{n+1} \binom{n+1}{k} z^k \\ &= \frac{1}{(n+1)z} \left( -1 + \sum_{k=0}^{n+1} \binom{n+1}{k} z^k \right) \\ &= \frac{(1+z)^{n+1} - 1}{(n+1)z}. \end{align*} \]