这个数学的网，编得我有点晕

awei

\[\sum_{n=1}^{\infty}2^{-n}\times\frac{1-sign\left[ \sin\left( 2n-1\right)\right]-2\times sign\left[ \sin\left( 2n\right)\right]}{2}=0\]
\[\sum_{n=1}^{\infty}2^{-n}\times\frac{1-sign\left[ \sin\left( 2n-1\right)\right]}{2}-\sum_{n=1}^{\infty}2^{-n}\times sign\left[ \sin\left( 2n\right)\right]=0\]
有些晕化简后还是看得明了些,该怎么理解呢，有些晕

awei

可以再简化成这样，究竟是为什么呢
\[\sum_{n=1}^{\infty}2^{-n}\times sign\left[ \sin\left( 2n-1\right)\right]+\sum_{n=1}^{\infty}2^{-n}\times sign\left[ \sin\left( 2n\right)\right]+\sum_{n=1}^{\infty}2^{-n}\times sign\left[ \sin\left( 2n\right)\right]\]
\[=\sum_{n=1}^{\infty}2^{-n}\times sign\left[ \sin\left( 2n-1\right)\right]+\sum_{n=1}^{\infty}2^{-n+1}\times sign\left[ \sin\left( 2n\right)\right]\]
\[=\sum_{n=1}^{\infty}2^{-n}\times \left\{ sign\left[ \sin\left( 2n-1\right)\right]+2 \times sign\left[ \sin\left( 2n\right)\right]\right\}\]
\[=1\]