Problem 1547 (difficulty: 4/10)

Show that if \(\displaystyle f\) is the sum of a power series that converges on a disc of radius \(\displaystyle R\) around \(\displaystyle z_0\) then the average of \(\displaystyle f\) around a circle of radius \(\displaystyle r<R\) centered at \(\displaystyle z_0\) is \(\displaystyle f(z_0)\).

Give me another random problem!