Variance of log return

Question

Suppose $C_i$ is i-day's closed price, when drift is small, we have the close to close variance $$\sigma^2 =\dfrac{1}{n}\sum\limits^n_{i = 1}\left(\log\left(\dfrac{C_i}{C_{i-1}}\right)\right)^2.$$ If we adjust this for the drift, $$\sigma^2 =\dfrac{1}{n-1}\sum\limits^n_{i = 1}\left(\left(\log\left(\dfrac{C_i}{C_{i-1}}\right)\right)^2 - \dfrac{\log\left(\left(\dfrac{C_n}{C_0}\right)\right)^2}{n(n-1)}\right).$$ I don't know how to obtain the later one in the bracket? I know the original one should be $$\left(\log\left(\dfrac{C_i}{C_{i-1}}\right) - \dfrac{\log\left(\dfrac{C_n}{C_0}\right)}{n}\right)^2$$