Exercise 7.6.18

Question

Show that, under these circumstances, the sum of the lengths of the intervals making up each $C_n$ no longer tends to zero as $n \to \infty$. What is this limit?

Ulisse Mini · Accepted Answer

$$\sum^\infty_{n=1} 2^{n-1} \left(\frac{1}{3^{n+1}}\right) = \frac{1}{9}\sum^\infty_{n=1} \left(\frac{2}{3}\right)^{n-1} = \frac{1}{3}$$

Exercise 7.6.18

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Exercise 7.6.18

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