In $w_{k + 1}  w_k = (\frac{1  p}{p})^{exponent}(w_1  w_0)$, why isn't exponent $k + 1$?
Please see the $r^k$ underlined in red, which is $(\frac{1  p}{p})^k$ as defined by the green underlines.

How do you deduce that the exponent must be $k$? Why isn't the exponent $k + 1$?

Is this question related to the Fence Post Error? Have I committed it?
Tsitsiklis, Introduction to Probability (2008 2e), p 63.
1 answer
If you set $k=0$ the equation becomes $$w_{0+1}  w_0 = r^{\textrm{exponent}}(w_1w_0)$$ For this equation to hold (in general) the exponent must be zero and not one. Thus an exponent of $k+1$ must be wrong.
I think the problem is not a fencepost problem but the proper base case for the induction. Try to write down the step of going from $$w_{k+1}  w_k = r (w_kw_{k1})$$ to $$w_{k+1}  w_k = r^k (w_1w_0)$$ as a proper proof by induction.
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