Shouldn't there be a factor of $p$ on the right-hand side, for a result of $\mathbf P_1\{\tau_0 = \infty\} = p-q$ ? The source is Markov Chains and Mixing Times.
2026-03-28 00:27:36.1774657656
Is there an error in this text's computation?
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There is in fact an error, but it's on the left-hand side: The $p$ shouldn't be there. The right-hand side is OK. There's a corrected version here (p. $218$).