That technique on page 3 of splitting off one of the powers and taking the result to be equal to the original reminds me of the proof that 0.999...=1 https://i

That technique on page 3 of splitting off one of the powers and taking the result to be equal to the original reminds me of the proof that 0.999...=1 https://i.imgur.com/ECYa380.png https://i.imgur.com/ECYa380.png