First, the probability of entering the left door is almost one as n goes large.(by an induction formula).
Then it can be derived
E(n+1)=E(n)+1.
Since E(1)=0.
Then E(100)=99.
Then it can be derived
E(n+1)=E(n)+1.
Since E(1)=0.
Then E(100)=99.
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