In the problem The Cantor Set, we met the Cantor set, which is the limit of Cn as n tends to infinity.


C_1, C_2, C_3



We can talk about the length of one of our sets Cn.
The set C1 has length 1.
The set C2 has length
2
3

, as this is the total length of the line segments in C2.

What are the lengths of C3, C4 and C5?

Can you find a general expression for the length of Cn?

By considering what happens as n tends to infinity, can you find the length of the Cantor set?