deletions | additions       diff --git a/section_Input_Output_Sequences_begin__.tex b/section_Input_Output_Sequences_begin__.tex  index fd1e83b..3a5d14d 100644  --- a/section_Input_Output_Sequences_begin__.tex  +++ b/section_Input_Output_Sequences_begin__.tex 
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2(x+0)/2,(x+1)/2,(x-1)/6,2(x+2)/6,2(x-2)/10,3(x+3)/10,3(x-3)/14,4(x+4)/14,4(x-4)/18,5(x+5)/18...  \end{equation}  which means the sequence for any expression of the form \begin{equation}  \underset{k=1}{\overset{2K_0}{\large K \normalsize}} \frac{g(k)}{x} \frac{g(k,K_0)}{x}  =\sum_{n=0}^\infty \frac{(-1)^n}{x^{2n+1}}\sum_{k=1}^{K_0} k^n\\ g(k)=\large g(k,l)=\large  \Bigg\{ \normalsize \begin{matrix}  K_0, l,  & k=1 \\ \frac{k(2K_0+k)}{8+16(k-2)}, \frac{k(2l+k)}{8+16(k-2)},  & k=\mathrm{even} \\ \frac{(k-1)(2K_0-(k-1))}{8+16(k-2)}, \frac{(k-1)(2l-(k-1))}{8+16(k-2)},  & \mathrm{otherwise} \end{matrix}  \end{equation}