Sstrhsrtj

begin{align*}

sum_{j=1}^{m_0-1},(-1)^{j-1}hspace{-3ex} 

sum_{substack{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_{j+2} leq k_1 leq boldsymbol{ell} \ k_2 < cdots < k_j < k_{j+1} leq k_1 }} 

= sum_{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_2 leq k_1 leq 

 boldsymbol{ell}, } tag(3) label{eq:3}

end{align*}

which is very close to our goal, equation eqref{eq:2}. 

Comparing equation eqref{eq:3} with equation eqref{eq:2}, we discover that both have the identical 1ts{st} through $(m_0 -2)$ts{th} terms ($1 leq j leq m_0-2$). 

The only difference of the two is that the $(m_0 -1)$ts{th} term in equation eqref{eq:3} is ...

end{document}

begin{align*}

sum_{j=1}^{m_0-1},(-1)^{j-1}hspace{-3ex} 

sum_{substack{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_{j+2} leq k_1 leq boldsymbol{ell} \ k_2 < cdots < k_j < k_{j+1} leq k_1 }} 

= sum_{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_2 leq k_1 leq 

 boldsymbol{ell}, } tag(3) label{eq:3}

end{align*}

which is very close to our goal, equation eqref{eq:2}. 

Comparing equation eqref{eq:3} with equation eqref{eq:2}, we discover that both have the identical 1ts{st} through $(m_0 -2)$ts{th} terms ($1 leq j leq m_0-2$). 

The only difference of the two is that the $(m_0 -1)$ts{th} term in equation eqref{eq:3} is ...

end{document}

begin{align*}

sum_{j=1}^{m_0-1},(-1)^{j-1}hspace{-3ex} 

sum_{substack{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_{j+2} leq k_1 leq boldsymbol{ell} \ k_2 < cdots < k_j < k_{j+1} leq k_1 }} 

= sum_{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_2 leq k_1 leq 

 boldsymbol{ell}, } tag(3) label{eq:3}

end{align*}

which is very close to our goal, equation eqref{eq:2}. 

Comparing equation eqref{eq:3} with equation eqref{eq:2}, we discover that both have the identical 1ts{st} through $(m_0 -2)$ts{th} terms ($1 leq j leq m_0-2$). 

The only difference of the two is that the $(m_0 -1)$ts{th} term in equation eqref{eq:3} is ...

end{document}

begin{align*}

sum_{j=1}^{m_0-1},(-1)^{j-1}hspace{-3ex} 

sum_{substack{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_{j+2} leq k_1 leq boldsymbol{ell} \ k_2 < cdots < k_j < k_{j+1} leq k_1 }} 

= sum_{ k_{m_0 +1} leq k_{m_0} leq cdots leq k_2 leq k_1 leq 

 boldsymbol{ell}, } tag(3) label{eq:3}

end{align*}

which is very close to our goal, equation eqref{eq:2}. 

Comparing equation eqref{eq:3} with equation eqref{eq:2}, we discover that both have the identical 1ts{st} through $(m_0 -2)$ts{th} terms ($1 leq j leq m_0-2$). 

The only difference of the two is that the $(m_0 -1)$ts{th} term in equation eqref{eq:3} is ...

end{document}

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