# Prove this limit

• Nov 10th 2009, 06:11 AM
concern
Prove this limit
Hello, can anyone give any hint regarding this? I'm lost.

Prove that if Lim an = p
n-->infinity
then,
Lim ( a1 + a2+ .......an )/n = p
n-->infinity

Can't get started.
• Nov 10th 2009, 07:59 AM
concern
hey, can we use supremum and infemum concept here?
• Nov 10th 2009, 08:51 AM
Opalg
Quote:

Originally Posted by concern
Hello, can anyone give any hint regarding this? I'm lost.

Prove that if Lim an = p
n-->infinity
then,
Lim ( a1 + a2+ .......an )/n = p
n-->infinity

Can't get started.

Replacing $a_n$ by $b_n = a_n - p$ (for all n), you reduce the problem to the case where p=0. The proof for that case is given in this thread.
• May 5th 2013, 06:22 PM
Marissa043
Re: Prove this limit
I actually have to solve this same problem, and I clicked on "this thread" but it just brought me to the general page of all the threads. I've been trying to find it but I'm not getting anywhere, is there a more specific location I can find the thread that solves this problem? :) Please help!!
• May 6th 2013, 10:03 AM
Opalg
Re: Prove this limit
As the link to my previous solution to this problem no longer seems to work, I have posted a response to this thread at

$\text{http://www.mathhelpb}\hspace{0.01pt}\text{oards.com/f52}$