Total number of level=$k$
At level 0 number of node=$ 2^{0} $
At level 1 number of node =$2^{1}$
At level 2 number of node =$2^{2}$
At level 3 number of node =$2^{3}$
At level 4 number of node =$2^{4}$
At level 5 number of node =$2^{5}$..
.
.
.
.At level k number of node =$2^{k-1}$
Total number of node in complete binary tree=$ 2^{0} $+$2^{1}$+$2^{2}$+$2^{3}$+$2^{4}$.....................$2^{k-1}$
$\left \{ 1(2^{k}-1)/2-1\right \}$
=$2^{k}-1$