Two "Heads" are better than one
I toss a fair coin 100 times in a row. If the expected number of times that two Heads are tossed consecutively is equal to \(N\), what is the value of \(100N\)?
Clarification: A run of three or more Heads in a row will contribute more than one instance of consecutive Heads. If three Heads are tossed in a row, then two Heads have been tossed consecutively twice. If six Heads are tossed in a row, then two Heads have been tossed consecutively five times, and so on. For example, two Heads have been tossed consecutively 11 times in the following sequence of 30 tosses:
\[ THHTHHHHTHHHTHTHHHHHTTTTHHTHTT \]