since there are N leaves...

N/2 leaves(i will call nodes) will share only root. why? (they are on the 
other side of the root)
N/4 leaves share 2 nodes
N/8 leaves share 3 nodes...
so on...

= there are N paths, as there are N leaves, (or N-1 to be precise.. 
excluding leaf v )==>

so.. its N/2 * 1 + N/4 * 2 + N/8 * 3 + .... N/2^(log N) * log N == total..

dividing it by N, or(N-1 gives)

Sum(1 -> log N) (k/2^k)

can some one provide the final value for the above recurrence equation.

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