Let k P N$.$ Analytically, $(1+2^-$k$)-1=2^-$k$.$ Numerically, however,

it is not true for sufficiently large k due to roundoff errors. For instance,

$>>(1+2^(-100))-1$

ans $=0$

Using a while$-$loop, find the smallest natural number k such that $(1+2^(-$k$))-1$ evaluates

to $0$ in MATLAB. Then evaluate $2$k for the value of k found.