Chapter 11.2, Problem 70E

To determine

(a) We need to show that at $N^{th}$ stage, each remaining section has length less than $\raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$2^N$}\right.$ and that the total amount of table removed is $L\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\mathrm{...}+\frac{1}{2^{N+1}}\right)$

(b) We need to show that as the limit $N\to \infty$ preciously one half of the table remains.