## 2^n – 1 in base 2, n is a positive integer

$2^2 \; - \; 1 \; = \; 3 \; = \; 11_2$

$2^3 \; - \; 1 \; = \; 7 \; = \; 111_2$

$2^4 \; - \; 1 \; = \; 15 \; = \; 1111_2$

$2^5 \; - \; 1 \; = \; 31 \; = \; 11111_2$

$2^6 \; - \; 1 \; = \; 63 \; = \; 111111_2$

How does this show that    $2^n - 1 = 111...11_2$ ?