In Feynman's lectures, section 6.3, I follow most of his argument about a random walk, but I miss one step. To summarize, he's discussing a one-dimensional random walk (eg, determined by coin flips), and his notation is
$N$: steps taken
$D_N$: net distance from start at step $N$ for a given trial
$⟨D^2_N⟩$: expected value for $D_N$ (mean square distance)
I follow him as he shows
Then he says it follows that
I suppose this last step should be easy, but it's the one I don't follow! I'd appreciate any help. TIA.