# A Random Walk

**Discrete Mathematics**Level 5

Brilli the ant decides to have a walk along an infinitely long 1D line. For each step he takes, he would either walk forward or backwards by a distance of 1 with equal probability. Given that the expected displacement Brilli the ant would travel after \(k\) steps is \(E_k\), find

\[\lim _{ k\to\infty }{ \frac{2k}{E_k^2} }\]