# Math Help - binary tree math proof

1. ## binary tree math proof

a binary tree has leaves l1,l2,..lm
and for each leaf their depth is d1,d2,..dm

prove that
$\sum ^m_{i=1} 2^{-d_i}\leq1$
?
i dont know how to prove it

i know that the height of a binary tree is lgn
and that the number of nodes on a certain level is less then $2^n-1$
(the algebric series sum sum)