Lecture 6 slide 29

regarding the proof for the potential function decrease in slide 29 in the last step I don't understand why that expression simplifies to 0. Shouldn't we multiply x_t by a factor (t+3) instead of (t+2) and also isn't there a -y_t missing?
Thank you.

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as a student I would say:

\((t+2) x_t - t y_t -2z_t = (t+2) [\frac{t}{t+2} y_t + \frac{2}{t+2} z_t] -t y_t - 2z_t = 0 \)

Remark: formula in slide 25 are given at step t+1.

I don't know if it fully answers your question...

Thanks for your great answer, Adrien!

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