Piecewise constant approximation

Let s(t) be a continuous bandlimited signal. Let p(t) be its best
piecewise constant approximation on the uniformly partitioned unit
interval [0,1],

i.e p(t) = \sum_{i=1}^n c_i I_i(t)

where I_i(t) is the indicator function which takes 1 on the interval
[(i-1)/n , i/n) and 0 elsewhere.

Now how does the MSE ||s(t)-p(t)||^2 vary with n ?

Thanks,
er

.

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