a binary tree has leaves l1,l2,..lm

and for each leaf their depth is d1,d2,..dm

prove that

$\displaystyle \sum ^m_{i=1} 2^{-d_i}\leq1$

?

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 $\displaystyle 2^n-1$

(the algebric series sum sum)