Solution
= Solution
At time $T_k$ the visited vertices form a contiguous arc and the walk is at an endpoint. Exiting an interval of $k$ visited vertices, starting one step from an absorbing endpoint, has mean $k$. Therefore $\mathbb E(T_{k+1}-T_k)=k$ and $\mathbb ET_n=\sum_{k=1}^{n-1}k=n(n-1)/2$.