Tree 12

Probability Level 1

How many line-segments are there in the 12th (bottom right) image of this growing tree sequence?

2 12 − 1 2^{12}-1 1 2 2 + 1 12^{2+1} 2 12 + 1 2^{12}+1 1 2 2 − 1 12^2-1 2 12 − 1 2^{12-1}

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Zandra Vinegar by Zandra Vinegar

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1 solution

Zulqarnain Ansari
Aug 12, 2015

The sequence so obtained by this gif is (2-1), (2^2 -1), (2^3 - 1),..........,(2^12 -1) Hence the required number of line segments = (2^12 - 1) = 4095

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