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In the problem The Cantor Set, we met the Cantor set, which is the limit of $C_n$ as $n$ tends to infinity.
We can talk about the length of one of our sets $C_n$.
The set $C_1$ has length 1.
The set $C_2$ has length $\frac{2}{3}$, as this is the total length of the line segments in $C_2$.
What are the lengths of $C_3$, $C_4$ and $C_5$?
Can you find a general expression for the length of $C_n$?
By considering what happens as $n$ tends to infinity, can you find the length of the Cantor set?
How Long Is the Cantor Set?
Age 11 to 14
Challenge Level 
In the problem The Cantor Set, we met the Cantor set, which is the limit of $C_n$ as $n$ tends to infinity.
We can talk about the length of one of our sets $C_n$.
The set $C_1$ has length 1.
The set $C_2$ has length $\frac{2}{3}$, as this is the total length of the line segments in $C_2$.
What are the lengths of $C_3$, $C_4$ and $C_5$?
Can you find a general expression for the length of $C_n$?
By considering what happens as $n$ tends to infinity, can you find the length of the Cantor set?
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