1 Mozilla/5.0 (Macintosh; Intel Mac OS X 10_14_6) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/81.0.4044.113 Safari/537.36 /rde/contents/library/ps2img/cgi-bin/eqn2gif.cgi 157.118.206.41 1587566021 2020/04/22 23:33:41 \begin{aligned}a_{n}=2\cdot 3^{n-1}-1\\ a_{n}=\dfrac {2}{3}\left\{ 1-\left( -\dfrac {1}{2}\right) ^{n-1}\right\} \\ a_{n}=3\cdot 2^{n-1}-n-1\\ a_{n}=\begin{cases}3^{n}\left( \dfrac {1}{2}n\left( n-1\right) +3\right) \left( n\geqq 2\right) \\ 3\left( n=1\right) \end{cases}\end{aligned} \\ \begin{aligned}an=\dfrac {2}{2\cdot 3^{n-1}+1}\\ a_{n+2}-4a_{n+1}+3a_{n}=0\\ a_{n}=\dfrac {1}{2}\left( 3^{n-1}+1\right) \\ b_{n}=\dfrac {1}{2}\left( 3^{n-1}-1\right) \\ a_{n}=\dfrac {1}{3}n\left( n+1\right) \left( n+2\right) \\ \dfrac {1}{2}n\left( n+1\right) \\ n^{3}\end{aligned}\\ \begin{aligned}32-4\\ \dfrac {3}{4}-\dfrac {1}{2\left( n+1\right) \left( n+2\right) }\\ \dfrac {1}{4}n\left( n+1\right) \left( n+2\right) \left( n+3\right) \\ a_{n}=\left( \sqrt {2}\right) ^{n-4}\left\{ 4\sqrt {2}+5+\left( -1\right) ^{n-1}\left( 4\sqrt {2}-5\right) \right\} -3\\ a_{n}=\begin{cases}\left( \sqrt {2}\right) ^{n+3}-3\left( n=2k\right) \\ 5\cdot \left( \sqrt {2}\right) ^{n-2}-3\left( n=2k-1\right) \end{cases}\end{aligned}\\ 2 <IMG SRC="../cgi-cache/20200422_233327.gif"> 変換 正常に処理されました 使用できないTeXコマンドがありました \begin{aligned} \dfrac \dfrac \begin{cases} \dfrac \geqq \end{cases} \end{aligned} \begin{aligned} \dfrac \dfrac \dfrac \dfrac \dfrac \end{aligned} \begin{aligned} \dfrac \dfrac \dfrac \begin{cases} \end{cases} \end{aligned} 20200422_233327 http://www.mech.tohoku-gakuin.ac.jp/rde/contents/library/ps2img/eqn2gif_online.html Wed Apr 22 23:33:41 2020