Cauchy product

We'll wrap up this week with one more Analysis post before switching back to Stats next week.

A Cauchy Product of two series Σa_n, and Σb_n is the series Σc_n where

c_n = a₀b_n + a₁b_n-1 + ...+ a_nb₀

I'll be pretty surprised if this turns up on the Q, but there is one important result that comes out of this: if the two series are absolutely convergent, then the Cauchy product series is also absolutely convergent.