I apologize if this is in the wrong subject, but it is for my calculus class.

(a) Let Let , i.e., partial sums of from n = 1 to infinity.

Furthermore, let

Prove:

If then as well.

(b) The are called Cesaro sums, and the process is called Cesaro summation. It is used when the original sequence converges slowly or when a series does not have convergent partial sums. For example the series:

does not have convergent partial sums but does converge. Find the Cesaro limit ( )

of the sequence.