Silverman–Toeplitz theorem

Silverman-Toeplitz theorem is a way of telling us something about how quickly a sequence is converging to a limit. It tells us that if a certain special kind of matrix (called a Toeplitz matrix) is associated with the sequence, then the rate of convergence is at least as fast as the rate of convergence of the corresponding sequence of partial sums. Most of the time, this rate of convergence is very fast.