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18.014ESG Problem Set 11 Pramod N. Achar
 

Summary: 18.014­ESG Problem Set 11
Pramod N. Achar
Fall 1999
Monday
1. Let a : Z+
R be a sequence, and form the new sequence : Z+
R,
called its Cesaro sequence, or its sequence of arithmetic means, by
n =
a1 + · · · + an
n
=
1
n
n
k=1
ak.
(a) Show that if {an} converges, say limn an = A, then limn n =
A as well. (Hint: First prove it in the special case that A = 0. You
need to show, for any given > 0, how to choose an N > 0 such that

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics