One moving point in the coordinate plane can move right or up one position. $N$ is a number of all paths : paths that moving point starts from $(0, 0)$, without passing $(1, 0), (2, 1), . . . , (n, n-1)$ and moves $2n$ times to $(n, n)$. $a_k$ is a number of special paths : paths include in $N$, but $k$th moves to the right, $k+1$th moves to the up. find $$\frac{1}{N} (a_1+a_2+ . . . + a_{2n-1})$$