How many line-segments are there in the 4th image of this growing tree sequence?
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The number of line-segments in the first image = 1
The number of line-segments in the second image = 1 + 2
The number of line-segments in the third image = 1 + 2 + 4
The number of line-segments in the fourth image = 1 + 2 + 4 + 8 = 1 5
A generalization: The number of line-segments in the n t h image = 1 + 2 + 4 + … + 2 n − 1 = 2 n − 1 .