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[latex]\left[\begin{array}{c}\begin{array}{ccccc}b_{1j}&&&&\\&\ddots&&&\\&&b_{1j}&&\\&&&\ddots&\\&&&&b_{1j}\end{array}\\\begin{array}{ccccc}\cdots&\cdots&\cdots&\cdots&\cdots\end{array}\\\begin{array}{ccccc}&&\vdots&&\end{array}\\\begin{array}{ccccc}\cdots&\cdots&\cdots&\cdots&\cdots\end{array}\\\begin{array}{ccccc}b_{2j}&&&&\\&\ddots&&&\\&&b_{2j}&&\\&&&\ddots&\\&&&&b_{2j}\end{array}\end{array}\right][/latex]

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12Â¥: Originally posted by Á¿ÕÅ at 2015-12-30 10:10:24
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$$ \begin{align} \begin{array}{ccc} \left[ \begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array}\right. & \begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array} &\overbrace{ \left.\begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array}\right] }^{12345} \end{array} &=\color{#cc0000}{A\cdot\sum_{k=1}^\infty\left(\frac3{2k-1}-\frac3{2k}\right)}\\ &+\color{#02a100}{\begin{array}{ccc} \underbrace{\left\{\left[ \begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array}\right.\right.}_{12345} & \begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array} &\overbrace{ \left.\begin{array}{ccc} a& &\\ &\ddots&\\ &&b \end{array}\right] }^{12345} \end{array} }\\ \end{align}{\tag {81}} $$

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