Clarification in solution 2.36

[ChethanM555]

The first term in the solution will not simply so easily, because we are doing summation(xn-mu(N))^2 and not summation(xn-mu(N-1))^2. Using sequential expansion for mu(N) = mu(N-1) + (xn - mu(N-1))/N I'm getting the first term as (N-1)^3/N^3 * sigma^2(N-1). Can you please verify this?