Consider the sequence defined by \(a_k=\frac 1{k^2+k}\) for \(k\ge 1\). Given that \(a_m+a_{m+1}+\cdots+a_{n-1}=1/29\), for positive integers \(m\) and \(n\) with \(m < n\), find \(m+n\).

(第二十届AIME1 2002 第4题)