## All Tails (Solution)

As a function of \(n\), the average number of steps is

\[\frac{n^2+n}{4}\]Or put another way, if \(T_n\) in the \(n\)th triangular number (1,3,6,10,15,…), then the average number of steps is

\[\frac{T_n}{2}\]As a function of \(n\), the average number of steps is

\[\frac{n^2+n}{4}\]Or put another way, if \(T_n\) in the \(n\)th triangular number (1,3,6,10,15,…), then the average number of steps is

\[\frac{T_n}{2}\]